Problem 4 Using the Vertical-Line Test
Use the vertical-line test. Which graph(s) represent functions?
Graphs A and C fail the vertical-line test because for each graph, a vertical line passes through more than one point. They do not represent functions. Graph B does not fail the vertical-line test so it represents a function.
Think
Is a relation a function if it passes through the y-axis twice?
No; the y-axis is a vertical line so the relation fails the vertical-line test.
✓ Got It?
- Use the vertical-line test. Which graph(s) represent functions?
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A function rule is an equation that represents an output value in terms of an input value. You can write a function rule in function notation. Shown below are examples of function rules.
The independent variable, x, represents the input of the function. The dependent variable, f(x), represents the output of the function. It is called the dependent variable because its value depends on the input value.
Problem 5 Using Function Notation
For
Plan
How do you find the output?
Substitute the input into the function rule and simplify.
| x Input | Function Rule
|
f(x) Output |
|---|---|---|
|
|
|
11 |
| 0 |
|
5 |
|
|
|
|
✓ Got It?
- For
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- 0
- 5
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Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions