Function Worksheets - Free Printable

Let's solve each part of the worksheet step by step.

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A) Evaluate each function from the table.

We are given tables with values of $ x $ and $ f(x) $. We need to find specific function values based on the input $ x $.

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#### 1)
Table:
| $ x $ | -4 | 2 | 7 | 10 |
|--------|----|---|---|----|
| $ f(x) $ | 6 | 11 | 0 | 14 |

- i) $ f(-4) = ? $
Look at $ x = -4 $ → $ f(-4) = 6 $

- ii) $ f(7) = ? $
$ x = 7 $ → $ f(7) = 0 $

✔ Answers:
i) $ f(-4) = 6 $
ii) $ f(7) = 0 $

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#### 2)
Table:
| $ x $ | 5 | 8 | 13 | 19 |
|--------|---|---|----|----|
| $ f(x) $ | 37 | -13 | -55 | 22 |

- i) $ f(13) = ? $
$ x = 13 $ → $ f(13) = -55 $

- ii) $ f(8) = ? $
$ x = 8 $ → $ f(8) = -13 $

✔ Answers:
i) $ f(13) = -55 $
ii) $ f(8) = -13 $

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#### 3)
Table:
| $ x $ | -17 | -16 | -11 | 3 |
|--------|-----|-----|-----|---|
| $ f(x) $ | -27 | -17 | 1 | 29 |

- i) $ f(3) = ? $
$ x = 3 $ → $ f(3) = 29 $

- ii) $ f(-17) = ? $
$ x = -17 $ → $ f(-17) = -27 $

✔ Answers:
i) $ f(3) = 29 $
ii) $ f(-17) = -27 $

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#### 4)
Table:
| $ x $ | 0 | 4 | 10 | 14 |
|--------|---|---|----|----|
| $ f(x) $ | -16 | 99 | 0 | -8 |

- i) $ f(4) = ? $
$ x = 4 $ → $ f(4) = 99 $

- ii) $ f(14) = ? $
$ x = 14 $ → $ f(14) = -8 $

✔ Answers:
i) $ f(4) = 99 $
ii) $ f(14) = -8 $

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B) Evaluate the functions from the table.

Now we have two functions, $ f(x) $ and $ g(x) $, in the same table.

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#### 1)
Table:
| $ x $ | $ f(x) $ | $ g(x) $ |
|--------|-----------|-----------|
| 6 | 35 | 19 |
| 13 | -19 | 5 |
| 15 | 8 | 23 |

- i) $ f(13) = ? $
$ x = 13 $ → $ f(13) = -19 $

- ii) $ f(6) = ? $
$ x = 6 $ → $ f(6) = 35 $

- iii) $ g(15) = ? $
$ x = 15 $ → $ g(15) = 23 $

- iv) $ g(13) = ? $
$ x = 13 $ → $ g(13) = 5 $

- v) For what value of $ x $, $ f(x) $ is 35?
Find $ x $ such that $ f(x) = 35 $ → From table, $ x = 6 $

- vi) For what value of $ x $, $ g(x) $ is 5?
$ g(x) = 5 $ → $ x = 13 $

✔ Answers:
i) $ f(13) = -19 $
ii) $ f(6) = 35 $
iii) $ g(15) = 23 $
iv) $ g(13) = 5 $
v) $ x = 6 $
vi) $ x = 13 $

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#### 2)
Table:
| $ x $ | $ f(x) $ | $ g(x) $ |
|--------|-----------|-----------|
| -6 | -24 | 14 |
| 1 | 4 | -4 |
| 4 | 16 | 10 |

- i) $ f(4) = ? $
$ x = 4 $ → $ f(4) = 16 $

- ii) $ g(1) = ? $
$ x = 1 $ → $ g(1) = -4 $

- iii) $ g(4) = ? $
$ x = 4 $ → $ g(4) = 10 $

- iv) $ f(-6) = ? $
$ x = -6 $ → $ f(-6) = -24 $

- v) For what value of $ x $, $ f(x) $ is -24?
$ f(x) = -24 $ → $ x = -6 $

- vi) For what value of $ x $, $ f(x) $ is 4?
$ f(x) = 4 $ → $ x = 1 $

✔ Answers:
i) $ f(4) = 16 $
ii) $ g(1) = -4 $
iii) $ g(4) = 10 $
iv) $ f(-6) = -24 $
v) $ x = -6 $
vi) $ x = 1 $

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✔ Final Answers Summary:

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#### A)

1)
i) $ f(-4) = 6 $
ii) $ f(7) = 0 $

2)
i) $ f(13) = -55 $
ii) $ f(8) = -13 $

3)
i) $ f(3) = 29 $
ii) $ f(-17) = -27 $

4)
i) $ f(4) = 99 $
ii) $ f(14) = -8 $

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#### B)

1)
i) $ f(13) = -19 $
ii) $ f(6) = 35 $
iii) $ g(15) = 23 $
iv) $ g(13) = 5 $
v) $ x = 6 $
vi) $ x = 13 $

2)
i) $ f(4) = 16 $
ii) $ g(1) = -4 $
iii) $ g(4) = 10 $
iv) $ f(-6) = -24 $
v) $ x = -6 $
vi) $ x = 1 $

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