Alright parents and Secondary 4 (S4) students in Singapore, leh! Let's dive into the world of functions and graphs! This might sound intimidating, but trust me, with a little understanding of the basics, sketching graphs can be quite straightforward. How to solve function-related problems using graphical methods . In today's fast-paced educational landscape, many parents in Singapore are seeking effective strategies to enhance their children's grasp of mathematical principles, from basic arithmetic to advanced problem-solving. Building a strong foundation early on can greatly improve confidence and academic achievement, aiding students handle school exams and real-world applications with ease. For those exploring options like math tuition it's essential to focus on programs that highlight personalized learning and experienced instruction. This method not only resolves individual weaknesses but also cultivates a love for the subject, contributing to long-term success in STEM-related fields and beyond.. This guide is tailored to help you navigate the concepts relevant to the secondary 4 math syllabus singapore, as defined by the Ministry Of Education Singapore. We'll focus on how transformations affect the shapes of graphs, making it easier to visualise and sketch them.
First things first, we need to familiarise ourselves with the "OGs" of the function world – the base functions. Think of these as the templates upon which all other, more complex graphs are built. Knowing these well is like knowing the alphabet before you start writing essays for your English paper. Got it?
f(x) = x (or y = x), this is a straight line passing through the origin (0,0) with a slope of 1. Any function of the form f(x) = mx + c is a linear function, where 'm' is the gradient (slope) and 'c' is the y-intercept (where the line cuts the y-axis).f(x) = x2. The graph is a U-shaped curve. The key features are its vertex (the minimum or maximum point) and its axis of symmetry.f(x) = x3, the cubic function has a characteristic S-shape. In the city-state's challenging education framework, parents fulfill a crucial role in guiding their youngsters through key assessments that form scholastic paths, from the Primary School Leaving Examination (PSLE) which examines basic abilities in disciplines like mathematics and scientific studies, to the GCE O-Level exams focusing on intermediate mastery in diverse fields. As learners advance, the GCE A-Level assessments demand more profound analytical abilities and subject mastery, often determining university entries and occupational directions. To remain well-informed on all elements of these national assessments, parents should explore authorized resources on Singapore exams offered by the Singapore Examinations and Assessment Board (SEAB). This secures entry to the most recent syllabi, examination schedules, sign-up information, and instructions that align with Ministry of Education standards. Consistently referring to SEAB can assist households plan efficiently, minimize ambiguities, and bolster their children in reaching optimal results in the midst of the challenging environment.. It passes through the origin and has a point of inflection (where the curve changes its concavity).f(x) = √x, this function is only defined for non-negative values of x (x ≥ 0). It starts at the origin and increases gradually, forming a curve that hugs the x-axis.f(x) = |x|, this function returns the magnitude (positive value) of any input. In the rigorous world of Singapore's education system, parents are increasingly intent on arming their children with the abilities required to thrive in rigorous math programs, including PSLE, O-Level, and A-Level exams. Recognizing early indicators of challenge in subjects like algebra, geometry, or calculus can make a world of difference in developing tenacity and proficiency over complex problem-solving. Exploring reliable math tuition singapore options can offer personalized assistance that matches with the national syllabus, making sure students gain the edge they want for top exam performances. By emphasizing dynamic sessions and consistent practice, families can assist their kids not only satisfy but exceed academic goals, opening the way for future opportunities in demanding fields.. Its graph is a V-shaped, with the vertex at the origin.Understanding these "base models" is key to tackling more complex transformations. It's like knowing how a basic nasi lemak is made before you start adding fancy ingredients like lobster or truffle oil (ok, maybe not truffle oil in nasi lemak, but you get the idea!).
Fun Fact: Did you know that the concept of functions, as we understand it today, took centuries to evolve? While mathematicians like Nicole Oresme were playing with the idea of representing relationships graphically in the 14th century, it wasn't until the 17th century that mathematicians like Gottfried Wilhelm Leibniz started formalising the notation and terminology we use today!
Alright, parents and Secondary 4 students! Ever feel like your math graphs are just...stuck? Like they need a little nudge? Well, today we're diving into vertical translations – think of it as giving your graph a boost up, or a gentle slide down. In a digital time where continuous skill-building is essential for occupational advancement and personal development, prestigious universities globally are dismantling obstacles by providing a wealth of free online courses that cover varied subjects from informatics studies and commerce to social sciences and wellness disciplines. These initiatives permit learners of all backgrounds to utilize top-notch lectures, assignments, and resources without the monetary burden of standard registration, commonly through services that deliver flexible timing and engaging features. Exploring universities free online courses unlocks pathways to elite institutions' expertise, allowing self-motivated learners to improve at no cost and earn qualifications that enhance profiles. By making high-level learning readily available online, such initiatives promote international equity, empower marginalized populations, and cultivate creativity, demonstrating that quality education is progressively simply a tap away for anyone with web availability.. This is super relevant to the secondary 4 math syllabus singapore, so pay attention lah!
Basically, vertical translation is all about moving the entire graph of a function either upwards or downwards along the y-axis. We're not stretching it, squishing it, or flipping it – just sliding it! This is a fundamental concept in understanding Functions and Graphs, a key topic in the secondary 4 math syllabus singapore. So, let's get started!
The Basic Idea: f(x) + c and f(x) - c
The magic formula for vertical translations is surprisingly simple:
Where 'c' is just a constant number. Easy peasy, right?
Examples to Make it Crystal Clear
Let's say we have a simple function: f(x) = x2 (a parabola). This is a good example to understand as quadratic functions are part of the secondary 4 math syllabus singapore.
Think of it like this: if you were drawing the graph on a piece of paper, you'd literally slide the entire paper up or down!
Visual Aids: Seeing is Believing
Imagine a graph of y = sin(x). Now, picture adding 1 to it: y = sin(x) + 1. The entire sine wave simply moves one unit upwards. The peaks are higher, the valleys are higher, everything is shifted up. Similarly, y = sin(x) - 1 would shift the wave down.
Key Points and Their Transformations
Focus on key points to visualize the shift. For example:
For instance, if f(2) = 5, then for g(x) = f(x) + 3, we know that g(2) = 5 + 3 = 8. The point (2,5) has moved to (2,8).
Fun Fact: Did you know that the concept of transformations, including vertical translations, is used extensively in computer graphics and animation? When you see a character jump in a video game, it's all thanks to mathematical transformations!
Why This Matters (Besides the Syllabus!)
Understanding vertical translations isn't just about acing your secondary 4 math syllabus singapore. It builds a foundation for more complex transformations and helps you visualize mathematical relationships. Plus, it shows you that math isn't just abstract formulas – it's about understanding how things change and move!
Shifts the entire graph to the left or right. Adding a constant inside the function's argument moves it left, while subtracting moves it right. This transformation affects the x-values of the function, causing a horizontal shift.
Shifts the entire graph upwards or downwards. Adding a constant to the function moves it up, while subtracting moves it down. The shape of the graph remains unchanged, only its vertical position is altered.
Stretches or compresses the graph vertically. Multiplying the function by a constant greater than 1 stretches it, while multiplying by a constant between 0 and 1 compresses it. This affects the y-values, changing the graph's height.
Horizontal translations can be a bit counter-intuitive, especially for secondary 4 math students tackling the Singapore math syllabus. When we see \( f(x + c) \), we might instinctively think the graph shifts to the right, but it actually shifts to the *left* by \( c \) units. Similarly, \( f(x - c) \) shifts the graph to the *right* by \( c \) units. Think of it like this: to achieve the same 'y' value, you need to input a smaller 'x' value if you're adding to 'x', hence the leftward shift.
In Singapore's rigorous education landscape, where English acts as the key channel of instruction and plays a crucial position in national assessments, parents are eager to help their children overcome frequent obstacles like grammar influenced by Singlish, vocabulary deficiencies, and issues in interpretation or essay creation. Establishing strong basic skills from elementary levels can greatly enhance confidence in tackling PSLE elements such as situational writing and oral expression, while high school learners benefit from specific exercises in literary review and debate-style papers for O-Levels. In Singapore's vibrant education landscape, where learners encounter considerable pressure to thrive in mathematics from early to higher stages, locating a tuition center that integrates proficiency with genuine zeal can make a huge impact in nurturing a passion for the field. Enthusiastic educators who go past repetitive study to motivate critical reasoning and resolution skills are uncommon, however they are essential for helping pupils surmount challenges in areas like algebra, calculus, and statistics. For families hunting for similar dedicated guidance, Odyssey Math Tuition stand out as a symbol of devotion, motivated by teachers who are deeply engaged in individual student's journey. This consistent dedication converts into tailored lesson strategies that modify to unique demands, resulting in enhanced scores and a lasting fondness for math that spans into prospective educational and occupational pursuits.. For those seeking successful strategies, delving into english tuition singapore offers valuable information into curricula that match with the MOE syllabus and emphasize engaging education. This additional support not only hones assessment techniques through simulated exams and feedback but also supports home practices like everyday reading plus discussions to nurture long-term language mastery and academic success..The key to understanding horizontal shifts lies in recognizing that the constant is being added or subtracted *directly* from the 'x' value *before* the function is applied. This manipulation of the function's argument is what causes the horizontal movement. It's not a vertical shift, which would involve adding or subtracting a constant *after* the function has been evaluated, like in \( f(x) + c \). Pay close attention to whether the constant is inside or outside the parentheses with 'x'.
Imagine a basic graph like \( y = x^2 \). Now consider \( y = (x - 2)^2 \). This new graph looks exactly like the original parabola, but it's been shifted 2 units to the right. The vertex, originally at (0,0), is now at (2,0). Similarly, \( y = (x + 3)^2 \) shifts the graph 3 units to the left, placing the vertex at (-3,0). Visualizing these shifts with simple graphs first can help solidify the concept.
When sketching graphs with horizontal translations, focus on identifying key points on the original graph. These might include the vertex of a parabola, intercepts, or any other significant feature. Then, apply the shift to these key points. For example, if you're shifting \( f(x) \) to \( f(x - 4) \), every 'x' coordinate of a key point will increase by 4. Plot the new points and connect them to create the translated graph.
Understanding horizontal translations is crucial for many topics in the secondary 4 math syllabus Singapore, including transformations of trigonometric functions and curve sketching. These transformations aren't just abstract concepts; they appear in various real-world applications, from modeling projectile motion to analyzing wave patterns. Mastering horizontal shifts gives students a powerful tool for understanding and manipulating functions, setting them up for success in more advanced math courses.
Alright, parents and Secondary 4 students in Singapore, let's talk about making graphs of functions taller or shorter – like stretching a piece of chewing gum or squashing a kueh!
We're diving into vertical stretching and compression, a key part of the secondary 4 math syllabus singapore. This concept falls under the broader topic of functions and graphs. In this island nation's highly demanding scholastic environment, parents are dedicated to bolstering their kids' success in crucial math tests, starting with the foundational challenges of PSLE where problem-solving and theoretical understanding are examined thoroughly. As pupils move forward to O Levels, they face increasingly complicated topics like geometric geometry and trigonometry that require accuracy and logical skills, while A Levels present advanced calculus and statistics needing deep comprehension and usage. For those resolved to giving their offspring an academic boost, finding the best math tuition customized to these curricula can change educational journeys through focused methods and specialized insights. This effort not only enhances assessment outcomes across all levels but also imbues lifelong quantitative mastery, creating pathways to prestigious schools and STEM fields in a intellect-fueled marketplace.. Understanding this will seriously level up your graph-sketching game!
Before we zoom into stretching and squashing, let's quickly recap what functions and graphs are all about. Think of a function like a machine: you feed it a number (the input, often 'x'), and it spits out another number (the output, often 'y' or f(x)). A graph is simply a visual representation of all these input-output pairs, plotted on a coordinate plane.
Functions and graphs aren't just abstract math concepts. They're used everywhere! From modelling population growth to designing bridges, functions help us understand and predict real-world phenomena. Mastering this area of the secondary 4 math syllabus singapore opens doors to many exciting fields.
Fun fact: Did you know that the concept of a function wasn't formally defined until the 17th century? Mathematicians like Leibniz and Bernoulli played key roles in developing the notation and understanding we use today.
Imagine you have a graph of a function, say f(x). Now, what happens if we multiply the entire function by a constant, let's call it 'a'? We get a new function: g(x) = a * f(x). This is where the magic happens!
If 'a' is greater than 1 (a > 1), we're vertically stretching the graph. Each y-value is multiplied by 'a', making the graph taller. It's like pulling the graph upwards from the x-axis.
For example, if f(x) = x2 and a = 2, then g(x) = 2x2. The parabola becomes "taller" and narrower.
Now, what if 'a' is between 0 and 1 (0 compressing the graph. Each y-value is multiplied by 'a', making the graph shorter. It's like squashing the graph downwards towards the x-axis.
Using the same example, if f(x) = x2 and a = 0.5, then g(x) = 0.5x2. The parabola becomes "shorter" and wider.
Interesting Fact: Vertical stretches and compressions are examples of transformations. Transformations are operations that change the size, shape, or position of a graph. Other transformations include translations (shifting the graph) and reflections (flipping the graph).
Let's look at some examples that might appear in your secondary 4 math syllabus singapore:
Pro-tip: When sketching, always pay attention to key points on the original graph, such as the x-intercepts, y-intercept, maximum points, and minimum points. These points will help you accurately sketch the transformed graph.
Understanding vertical stretches and compressions is crucial for tackling more complex graph transformations. It builds a solid foundation for topics like:
So, remember to practice, practice, practice! The more you sketch, the better you'll become at visualizing these transformations. Don't worry, lah, you can do it!
Alright, Singapore parents and Secondary 4 math students, let's talk about making graphs wider or narrower! We're diving into horizontal stretching and compression, which might sound intimidating, but trust me, it's not as cheem as it seems. This is crucial stuff for the secondary 4 math syllabus singapore, so pay attention hor!
Before we jump into stretching and compressing, let's quickly recap functions and graphs. Think of a function like a machine: you put something in (an 'x' value), and it spits something else out (a 'y' value). A graph is simply a visual representation of all the 'x' and 'y' pairs that the function produces. This is a fundamental concept in the secondary 4 math syllabus singapore.
Fun Fact: Did you know that the concept of a function wasn't formally defined until the 17th century? Mathematicians like Leibniz and Bernoulli played a key role in developing the notation and understanding we use today!
Now, let's get to the main event: horizontal stretching and compression. This happens when we mess around with the 'x' inside the function, like this: f(bx). The 'b' is the key player here.
Here's the important thing to remember: The effect of 'b' is inverse!
Think of it like this: if b is 2, you're essentially telling the function to do everything twice as fast, which squishes the graph horizontally. If b is 1/2, you're telling it to do everything half as fast, which stretches the graph horizontally. It's a bit counter-intuitive, I know!
Example: Let's say we have the function f(x) = x2. If we change it to f(2x) = (2x)2, the graph will be compressed horizontally by a factor of 1/2. If we change it to f(x/2) = (x/2)2, the graph will be stretched horizontally by a factor of 2.
Horizontal stretching and compression directly affect the x-intercepts of the graph. The y-intercept, however, remains unchanged (assuming there are no other transformations).
So, if the original graph of f(x) had an x-intercept at x = a, then the graph of f(bx) will have an x-intercept at x = a/b.
Interesting Fact: Understanding transformations of graphs is not just useful in math class! It also has applications in fields like signal processing, image manipulation, and even economics.
This concept is important because it builds a strong foundation for understanding more complex functions and transformations later on. The secondary 4 math syllabus singapore emphasizes a deep understanding of functions and their graphical representations. Mastering horizontal stretching and compression will give you a significant advantage when tackling more advanced topics.
Plus, being able to visualize how changing the equation affects the graph is a powerful skill. It helps you develop a more intuitive understanding of mathematics, which is always a good thing, right?
So there you have it! In Singapore's competitive educational landscape, parents committed to their kids' excellence in mathematics commonly prioritize comprehending the structured development from PSLE's foundational issue-resolution to O Levels' complex subjects like algebra and geometry, and moreover to A Levels' sophisticated concepts in calculus and statistics. Keeping aware about curriculum updates and assessment guidelines is crucial to offering the appropriate support at all level, making sure students develop self-assurance and attain top outcomes. For authoritative insights and resources, visiting the Ministry Of Education site can deliver useful news on regulations, programs, and educational methods tailored to local criteria. Engaging with these credible materials strengthens households to match family study with classroom requirements, fostering enduring progress in mathematics and further, while staying informed of the latest MOE programs for holistic learner development.. Horizontal stretching and compression demystified. Remember the inverse relationship, practice with different examples, and you'll be sketching graphs like a pro in no time. Don't be afraid to ask your teacher for help if you're still struggling – that's what they're there for! Can or not? Can one lah! Good luck with your secondary 4 math syllabus singapore!
Alright parents and Sec 4 students, leh! Ever wondered how a simple minus sign can turn your graph upside down or make it look in the mirror? We're diving into reflections – flipping graphs across the x and y axes. This is crucial stuff for your secondary 4 math syllabus Singapore, so pay close attention!
Imagine your graph is a butterfly. Now, picture a puddle of water underneath it. The reflection you see in the water is what happens when you reflect a graph across the x-axis. Mathematically, this means multiplying the entire function by -1. So, if you have f(x), the reflection becomes -f(x).
Example: Let's say f(x) = x2 (a happy, smiley parabola). Then -f(x) = -x2. The smiley face turns into a frowny face – reflected across the x-axis!
Visual Cue: Every y-coordinate changes its sign. If a point was at (2, 4), it moves to (2, -4).
This time, imagine a mirror standing vertically along the y-axis. The reflection you see is what happens when you reflect a graph across the y-axis. Here, you replace x with -x in the function. So, f(x) becomes f(-x).
Example: Consider f(x) = x3. Then f(-x) = (-x)3 = -x3. The graph is flipped horizontally.
Visual Cue: Every x-coordinate changes its sign. If a point was at (2, 8), it moves to (-2, 8).
Fun Fact: Did you know that some functions look the same even after reflection? These are called even functions (symmetric about the y-axis) and odd functions (symmetric about the origin). Think of a perfect circle centered at the origin – reflecting it across either axis doesn't change a thing!
Understanding reflections is just one piece of the puzzle when it comes to functions and graphs. Let's zoom out and see how it all fits together.
Functions are like machines: you put something in (an 'x' value), and you get something out (a 'y' value). In modern years, artificial intelligence has revolutionized the education sector globally by allowing customized learning journeys through responsive systems that adapt content to unique student speeds and approaches, while also automating evaluation and administrative responsibilities to release instructors for deeper impactful interactions. Internationally, AI-driven systems are bridging academic disparities in underserved locations, such as utilizing chatbots for linguistic acquisition in underdeveloped regions or analytical tools to identify vulnerable learners in the EU and North America. As the integration of AI Education achieves traction, Singapore shines with its Smart Nation project, where AI tools boost syllabus personalization and equitable instruction for multiple demands, including adaptive education. This method not only improves assessment outcomes and involvement in domestic classrooms but also corresponds with worldwide initiatives to cultivate lifelong skill-building competencies, preparing students for a innovation-led marketplace amid moral factors like data protection and fair access.. The graph is simply a visual representation of all these 'x' and 'y' pairs plotted on a coordinate plane.
There are many types of functions, each with its own unique graph:
Reflections are just one type of transformation. Others include:
Mastering these transformations is key to acing your secondary 4 math syllabus Singapore. It allows you to quickly sketch graphs without having to plot a million points!
Interesting Fact: The concept of functions wasn't always as clear as it is today. It took mathematicians centuries to develop a precise definition. Leonhard Euler, a Swiss mathematician from the 18th century, is often credited with formalizing the modern concept of a function.
The secondary 4 math syllabus Singapore emphasizes understanding transformations of graphs. You'll be expected to:
Think of it like this: understanding transformations gives you superpowers to manipulate and interpret graphs, which is super useful in various fields, from engineering to economics!
So, there you have it! Reflections are like looking in a mirror – they flip your graph across an axis. Understanding this, along with other transformations, will make your secondary 4 math syllabus Singapore a whole lot easier to navigate. Keep practicing, and you'll be graphing like a pro in no time! Can lah!
Keywords: secondary 4 math syllabus singapore, functions and graphs, transformations of graphs, reflections, x-axis reflection, y-axis reflection, graphing functions, math tuition singapore, O level math
Hey parents and students! Ever feel like sketching graphs is like trying to navigate a crowded MRT station during peak hour? Don't worry, lah! This guide will help you and your secondary 4 kiddos master graph transformations, making even the most complex functions feel like a breeze. We'll break down how to combine multiple transformations, step-by-step, so you can tackle those tricky secondary 4 math syllabus singapore questions with confidence.
Before we dive into transformations, let's quickly recap what functions and graphs are all about. Think of a function as a machine: you put something in (an input, usually 'x'), and it spits something else out (an output, usually 'y' or f(x)). A graph is simply a visual representation of all the possible inputs and outputs of that function. Understanding this basic relationship is key to understanding how transformations work.
The secondary 4 math syllabus singapore covers a range of functions. Here are a few common ones you'll encounter:
Fun Fact: Did you know that René Descartes, the famous philosopher, is credited with developing the coordinate system we use to graph functions? He was trying to find a way to link algebra and geometry!
Transformations are like applying filters to a photo – they change the look of the graph without changing the underlying function. The key is to understand how each transformation affects the original graph.
Let's look at each type in more detail:
A translation shifts the entire graph without changing its shape. * Vertical Translation: Adding a constant 'c' to the function, f(x) + c, shifts the graph upwards if c > 0 and downwards if c Horizontal Translation: Replacing 'x' with 'x - c', f(x - c), shifts the graph to the right if c > 0 and to the left if c
A reflection flips the graph across an axis. * Reflection in the x-axis: Multiplying the function by -1, -f(x), reflects the graph over the x-axis. * Reflection in the y-axis: Replacing 'x' with '-x', f(-x), reflects the graph over the y-axis.
Stretches and compressions change the shape of the graph by either stretching it or compressing it. * Vertical Stretch/Compression: Multiplying the function by a constant 'a', a*f(x), stretches the graph vertically if a > 1 and compresses it if 0 Horizontal Stretch/Compression: Replacing 'x' with 'ax', f(ax), compresses the graph horizontally if a > 1 and stretches it if 0
Interesting Fact: Transformations are used extensively in computer graphics and animation to create realistic movements and perspectives. Think about how a character's movements are animated in a video game – transformations are at the heart of it!
This is where things can get a little tricky. When you have multiple transformations, the order in which you apply them matters! A good rule of thumb to remember is: **Horizontal Transformations, then Vertical Transformations (HV)**. Think of it like reading from left to right on the x-axis, then moving up or down on the y-axis.
Here's a more detailed breakdown:
Let's put this into practice with some examples. In this Southeast Asian hub's demanding education system, where educational success is paramount, tuition typically refers to supplementary additional sessions that provide focused assistance in addition to classroom programs, assisting pupils grasp disciplines and gear up for key tests like PSLE, O-Levels, and A-Levels during strong competition. This non-public education industry has developed into a lucrative business, powered by families' expenditures in tailored guidance to overcome knowledge deficiencies and enhance scores, although it commonly adds stress on adolescent learners. As artificial intelligence appears as a disruptor, investigating advanced tuition approaches uncovers how AI-driven tools are personalizing instructional experiences internationally, providing adaptive tutoring that surpasses standard practices in productivity and involvement while addressing global learning inequalities. In Singapore specifically, AI is disrupting the conventional tuition approach by enabling budget-friendly , flexible applications that match with national curricula, possibly lowering fees for households and improving achievements through analytics-based analysis, although ethical considerations like over-reliance on technology are examined.. We'll start with a basic function and then apply multiple transformations.
Example 1: Sketch the graph of y = 2(x - 1)² + 3, starting with the basic function y = x².
Example 2: Sketch the graph of y = -sin(2x) - 1, starting with the basic function y = sin(x).
Try sketching these examples yourself! It's a great way to solidify your understanding. Remember to label key points on your graph, such as the vertex of a parabola or the maximum and minimum points of a trigonometric function.
History: The study of transformations has roots in geometry and the development of analytic geometry by mathematicians like Descartes. Understanding how shapes and functions can be manipulated is fundamental to many areas of mathematics and science.
Here are some extra tips to help you excel in your secondary 4 math syllabus singapore:
With a little bit of practice and a solid understanding of the order of operations, you'll be sketching graphs like a pro in no time! Jiayou, students! You can do it!
A function transformation alters the graph of a function by shifting, stretching, compressing, or reflecting it. Understanding transformations is crucial for Secondary 4 students as it simplifies graphing complex functions and is a key concept in A-Level mathematics.
A vertical shift moves the entire graph up or down. Adding a constant c to the function, f(x) + c, shifts the graph up by c units, while subtracting c, f(x) - c, shifts it down by c units. Remember, + is up and - is down, similar to a lift in a building.
Vertical stretch/compression affects the y-values and is represented by a*f(x). If |a| > 1, its a vertical stretch; if 0 < |a| < 1, its a vertical compression. Horizontal stretch/compression affects the x-values and is represented by f(bx). If |b| > 1, its a horizontal compression; if 0 < |b| < 1, its a horizontal stretch. Note that horizontal transformations have the opposite effect of what you might expect.
Reflection over the x-axis changes the sign of the y-values, resulting in the function -f(x). The graph is flipped upside down. Reflection over the y-axis changes the sign of the x-values, resulting in the function f(-x). The graph is flipped left to right.
Use real-life examples! Show how stretching a rubber band (stretching), shrinking a photo on a phone (compression), or looking at a reflection in a mirror (reflection) are all transformations. You can also use graphing software to visually demonstrate how changing the equation changes the graph, making it more engaging for them.