functions tables and graphs grade 8 quiz

📚 Quick Study Guide

• 🔢 Function: A relation where each input (x-value) has only one output (y-value). You can think of it as a machine where you put something in, and you get a specific thing out.
• 📈 Tables: Organize input and output values. They help visualize the relationship between x and y. A table is a simple way to organize data.
• 📊 Graphs: Visual representations of functions. The x-axis is usually the input, and the y-axis is the output. Key points to remember are slope and intercepts.
• ✍️ Linear Equations: Equations that form a straight line when graphed. The standard form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• 🧭 Slope: The steepness of a line, calculated as rise over run (change in y divided by change in x), often written as $m = \frac{\Delta y}{\Delta x}$.
• 📍 Y-Intercept: The point where the line crosses the y-axis. It's the value of y when x is 0.
• 📝 Function Notation: A way to represent functions using $f(x)$, where $f(x)$ represents the output for a given input $x$. For example, $f(x) = 2x + 3$.

🧪 Practice Quiz

1. What is a function?
   1. A relation where each input has one output.
   2. A relation where each output has one input.
   3. Any set of ordered pairs.
   4. A straight line on a graph.
2. Which of the following equations represents a linear function?
   1. $y = x^2 + 1$
   2. $y = \frac{1}{x}$
   3. $y = 2x - 3$
   4. $y = \sqrt{x}$
3. What does 'm' represent in the linear equation $y = mx + b$?
   1. Y-intercept
   2. X-intercept
   3. Slope
   4. Area
4. What is the slope of a line that passes through the points (1, 2) and (3, 6)?
   1. 1
   2. 2
   3. 3
   4. 4
5. What is the y-intercept of the line $y = 3x + 5$?
   1. 3
   2. 5
   3. 0
   4. 8
6. If $f(x) = x + 4$, what is the value of $f(2)$?
   1. 2
   2. 4
   3. 6
   4. 8
7. Which of the following is NOT a way to represent a function?
   1. Table
   2. Graph
   3. Equation
   4. List of Colors