Evaluating Exponential Functions Worksheets - Free Printable

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

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A) Evaluate each function at the specified value

#### 1) $ f(x) = 9^{(x - 10)} - x $, $ x = 10 $

Substitute $ x = 10 $:

$$
f(10) = 9^{(10 - 10)} - 10 = 9^0 - 10 = 1 - 10 = -9
$$

✔ Answer: $-9$

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#### 2) $ f(x) = 8 \cdot (-2)^{(-1 - x)} - 3x $, $ x = 2 $

Substitute $ x = 2 $:

$$
f(2) = 8 \cdot (-2)^{(-1 - 2)} - 3(2) = 8 \cdot (-2)^{-3} - 6
$$

Now compute $ (-2)^{-3} = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8} $

$$
f(2) = 8 \cdot \left(-\frac{1}{8}\right) - 6 = -1 - 6 = -7
$$

✔ Answer: $-7$

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#### 3) $ f(x) = -12 + 7^{(2x + 10)} $, $ x = -4 $

Substitute $ x = -4 $:

$$
f(-4) = -12 + 7^{(2(-4) + 10)} = -12 + 7^{(-8 + 10)} = -12 + 7^2 = -12 + 49 = 37
$$

✔ Answer: $37$

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#### 4) $ f(x) = x - 10^{-2x} $, $ x = -1 $

Substitute $ x = -1 $:

$$
f(-1) = -1 - 10^{-2(-1)} = -1 - 10^{2} = -1 - 100 = -101
$$

✔ Answer: $-101$

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B) Evaluate each function

#### 1) If $ f(x) = 10 \cdot 4^{x} - 11 $, find $ f(-2) $

$$
f(-2) = 10 \cdot 4^{-2} - 11 = 10 \cdot \frac{1}{4^2} - 11 = 10 \cdot \frac{1}{16} - 11 = \frac{10}{16} - 11 = \frac{5}{8} - 11
$$

Convert to common denominator:

$$
= \frac{5}{8} - \frac{88}{8} = -\frac{83}{8}
$$

✔ Answer: $-\frac{83}{8}$ or $-10.375$

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#### 2) If $ f(x) = 4^{(x - 2)} + 1 $, find $ f(3) $

$$
f(3) = 4^{(3 - 2)} + 1 = 4^1 + 1 = 4 + 1 = 5
$$

✔ Answer: $5$

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#### 3) If $ f(x) = 13 \cdot (-5)^{(x + 1)} $, find $ f(-8) $

$$
f(-8) = 13 \cdot (-5)^{(-8 + 1)} = 13 \cdot (-5)^{-7}
$$

$$
(-5)^{-7} = \frac{1}{(-5)^7} = \frac{1}{-78125} = -\frac{1}{78125}
$$

So,

$$
f(-8) = 13 \cdot \left(-\frac{1}{78125}\right) = -\frac{13}{78125}
$$

✔ Answer: $-\frac{13}{78125}$

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#### 4) If $ f(x) = -7 + (-1)^{(x - 5)} $, find $ f(-5) $

$$
f(-5) = -7 + (-1)^{(-5 - 5)} = -7 + (-1)^{-10}
$$

Note: $ (-1)^{-10} = \frac{1}{(-1)^{10}} = \frac{1}{1} = 1 $

So,

$$
f(-5) = -7 + 1 = -6
$$

✔ Answer: $-6$

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C) What is the value of $ f(0) $ if $ f(x) = (-6)^{(2 - 5x)} + x $?

Substitute $ x = 0 $:

$$
f(0) = (-6)^{(2 - 5(0))} + 0 = (-6)^2 + 0 = 36
$$

✔ Answer: $36$

So the correct choice is:
i) 36

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✔ Final Answers Summary:

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A)
1) $-9$
2) $-7$
3) $37$
4) $-101$

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B)
1) $-\frac{83}{8}$
2) $5$
3) $-\frac{13}{78125}$
4) $-6$

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C) $ f(0) = 36 $ → Answer: (i) 36

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