Solved Examples for Introducing Functions in 8th Grade Math

📚 Quick Study Guide

• 🔢 What is a Function? A function is a special type of relation where each input (x-value) has only one output (y-value). Think of it like a machine: you put something in, and it gives you only one specific thing out.
• 📈 Representing Functions: Functions can be shown in several ways:
  • 📝 Equations: Using formulas like $y = 2x + 1$.
  • 📊 Tables: Listing x and y values in a table.
  • 📍 Graphs: Plotting points on a coordinate plane.
  • 🗺️ Mapping Diagrams: Showing how each x-value maps to a y-value.
• ➕ Function Notation: We often use $f(x)$ to represent a function. So, $f(x) = 3x - 2$ means that if you input a value for $x$, you multiply it by 3 and then subtract 2 to get the output.
• 💡 Vertical Line Test: A graph represents a function if a vertical line drawn anywhere on the graph intersects it at only one point.
• 🎯 Domain and Range:
  • 📍 Domain: All possible input values (x-values) of a function.
  • 📍 Range: All possible output values (y-values) of a function.

📝 Practice Quiz

1. Which of the following represents a function?
   1. A. {(1, 2), (1, 3), (2, 4), (3, 5)}
   2. B. {(1, 2), (2, 2), (3, 2), (4, 2)}
   3. C. {(1, 2), (2, 3), (3, 4), (1, 5)}
   4. D. {(1, 2), (2, 3), (2, 4), (3, 5)}
2. If $f(x) = 4x - 3$, what is $f(2)$?
   1. A. 5
   2. B. 8
   3. C. 11
   4. D. -1
3. Which graph represents a function based on the vertical line test?
   1. A. A circle
   2. B. A vertical line
   3. C. A parabola opening sideways
   4. D. A parabola opening upwards
4. What is the domain of the function represented by the set of points {(0, 1), (1, 2), (2, 3), (3, 4)}?
   1. A. {1, 2, 3, 4}
   2. B. {0, 1, 2, 3}
   3. C. {0, 1, 2, 3, 4}
   4. D. { } (empty set)
5. Which equation represents a linear function?
   1. A. $y = x^2 + 1$
   2. B. $y = \frac{1}{x}$
   3. C. $y = 3x - 5$
   4. D. $y = |x|$
6. Given the function $f(x) = x^2 - 2x + 1$, what is $f(0)$?
   1. A. 0
   2. B. 1
   3. C. -1
   4. D. 2
7. Which of the following tables represents a function?
   1. A. x: 1, 2, 3; y: 4, 5, 4
   2. B. x: 1, 2, 1; y: 3, 4, 5
   3. C. x: 2, 3, 2; y: 5, 6, 7
   4. D. x: 4, 5, 6; y: 1, 2, 1