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# Introduction to Functions Help (page 2)

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By McGraw-Hill Professional
Updated on Oct 4, 2011

#### Examples

• Find f (5), f (−3), and f (0) for the function above.

For f (5), does x = 5 belong to x ≤ −2, −2 < x < 2, or x ≥ 2? Because 5 ≥ 2, we will use y = x 2, the formula written next to x ≥ 2.

f (5) = 5 2 = 25

For f (−3), does x = −3 belong to x ≤ −2, −2 < x < 2, or x ≥ 2? Because −3 ≤ −2, we will use y = x − 1, the formula written next to x ≤ −2.

f (−3) = −3 − 1 = −4

For f (0), does x = 0 belong to x ≤ −2, −2 < x < 2, or x ≥ 2? Because −2 < 0 < 2, we will use y = 2 x , the formula written next to −2 < x < 2.

f (0) = 2(0) = 0

• Find f (3), f (1), and f (−4) for

 f (3) = 5 because 3 > 1 f (1) = −1 because 1 ≤ 1 f (−4) = −(−4) = 4 because − 4 ≤ 1

Piecewise functions come up in daily life. For example, suppose a company pays the regular hourly wage for someone who works up to eight hours but time and a half for someone who works more than eight hours but no more than ten hours and double time for more than ten hours. Then a worker whose regular hourly pay is \$10 has the daily pay function below.

Below is an example of a piecewise function taken from an Internal Revenue Service (IRS) publication. The y -value is the amount of personal income tax for a single person. The x -value is the amount of taxable income.

A single person whose taxable income was \$30,120 would pay \$4341. (Source: 2003, 1040 Forms and Instructions)

## Introduction to Functions Practice Problems

### Practice

1. Find f (−1) and f (0) for f ( x ) = 3 x2 + 2 x − 1.
2. Evaluate at x = −3, x = 1, and .
3. Evaluate g at x = 6, x = 8, and x = 10.
4. Find f (5), f (3), f (2), f (0), and f (−1).

5. The function below gives the personal income tax for a single person for the 2003 year. If a single person had a taxable income of \$63,575, what is her tax?

### Solutions

1. f (−1) = 3(−1) 2 + 2(−1) − 1 = 3 − 2 − 1 = 0 f (0) = 3(0) 2 + 2(0) − = −1
2.

3.

4.

5. The tax is \$12,704 because 63,550 ≤ 63,575 < 63,600.

Practice problems for this concept can be found at: Introduction to Functions Practice Test.

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