Function Notation Worksheet - Free Printable

Problem Analysis:

The task involves solving function evaluation problems and determining inputs for given outputs. Let's solve each part step by step.

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1. Let \( g(x) = -5x + 2 \). Evaluate each of the following:

#### (a) \( g(1) = -3 \)
- Substitute \( x = 1 \) into \( g(x) = -5x + 2 \):
\[
g(1) = -5(1) + 2 = -5 + 2 = -3
\]
This is correct.

#### (b) \( g(-2) = 12 \)
- Substitute \( x = -2 \) into \( g(x) = -5x + 2 \):
\[
g(-2) = -5(-2) + 2 = 10 + 2 = 12
\]
This is correct.

#### (c) \( g(x) = -2 \)
- Solve for \( x \) when \( g(x) = -2 \):
\[
-5x + 2 = -2
\]
Subtract 2 from both sides:
\[
-5x = -4
\]
Divide by -5:
\[
x = \frac{4}{5}
\]

#### (d) \( g(x) = 17 \)
- Solve for \( x \) when \( g(x) = 17 \):
\[
-5x + 2 = 17
\]
Subtract 2 from both sides:
\[
-5x = 15
\]
Divide by -5:
\[
x = -3
\]

Final Answers for Part 1:
\[
\boxed{(a) -3, (b) 12, (c) \frac{4}{5}, (d) -3}
\]

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2. Let \( f(x) = 2x \). Evaluate each of the following:

#### (a) \( f(-2) \)
- Substitute \( x = -2 \) into \( f(x) = 2x \):
\[
f(-2) = 2(-2) = -4
\]

#### (b) \( f(6) \)
- Substitute \( x = 6 \) into \( f(x) = 2x \):
\[
f(6) = 2(6) = 12
\]

#### (c) \( f(-1.5) \)
- Substitute \( x = -1.5 \) into \( f(x) = 2x \):
\[
f(-1.5) = 2(-1.5) = -3
\]

#### (d) \( f(0.4) \)
- Substitute \( x = 0.4 \) into \( f(x) = 2x \):
\[
f(0.4) = 2(0.4) = 0.8
\]

Final Answers for Part 2:
\[
\boxed{(a) -4, (b) 12, (c) -3, (d) 0.8}
\]

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3. Suppose \( f(x) = 4x - 2 \). Determine \( x \) such that:

#### (a) \( f(x) = 18 \)
- Solve for \( x \) when \( f(x) = 18 \):
\[
4x - 2 = 18
\]
Add 2 to both sides:
\[
4x = 20
\]
Divide by 4:
\[
x = 5
\]

#### (b) \( f(x) = 0 \)
- Solve for \( x \) when \( f(x) = 0 \):
\[
4x - 2 = 0
\]
Add 2 to both sides:
\[
4x = 2
\]
Divide by 4:
\[
x = \frac{1}{2}
\]

#### (c) \( f(x) = -2 \)
- Solve for \( x \) when \( f(x) = -2 \):
\[
4x - 2 = -2
\]
Add 2 to both sides:
\[
4x = 0
\]
Divide by 4:
\[
x = 0
\]

#### (d) \( f(x) = 10 \)
- Solve for \( x \) when \( f(x) = 10 \):
\[
4x - 2 = 10
\]
Add 2 to both sides:
\[
4x = 12
\]
Divide by 4:
\[
x = 3
\]

Final Answers for Part 3:
\[
\boxed{(a) 5, (b) \frac{1}{2}, (c) 0, (d) 3}
\]

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4. Suppose \( h(x) = 4x \). Determine \( x \) such that:

#### (a) \( h(x) = 36 \)
- Solve for \( x \) when \( h(x) = 36 \):
\[
4x = 36
\]
Divide by 4:
\[
x = 9
\]

#### (b) \( h(x) = -4 \)
- Solve for \( x \) when \( h(x) = -4 \):
\[
4x = -4
\]
Divide by 4:
\[
x = -1
\]

#### (c) \( h(x) = 0 \)
- Solve for \( x \) when \( h(x) = 0 \):
\[
4x = 0
\]
Divide by 4:
\[
x = 0
\]

#### (d) \( h(x) = 20 \)
- Solve for \( x \) when \( h(x) = 20 \):
\[
4x = 20
\]
Divide by 4:
\[
x = 5
\]

Final Answers for Part 4:
\[
\boxed{(a) 9, (b) -1, (c) 0, (d) 5}
\]

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5. Use the table to find the following:

The table is as follows:
\[
\begin{array}{c|c}
X & Y \\
\hline
3 & 1 \\
2 & 4 \\
4 & 9 \\
5 & 25 \\
\end{array}
\]

#### (a) \( f(3) \)
- From the table, when \( X = 3 \), \( Y = 1 \):
\[
f(3) = 1
\]

#### (b) \( f(2) \)
- From the table, when \( X = 2 \), \( Y = 4 \):
\[
f(2) = 4
\]

#### (c) \( f(5) \)
- From the table, when \( X = 5 \), \( Y = 25 \):
\[
f(5) = 25
\]

#### (d) \( f(4) \)
- From the table, when \( X = 4 \), \( Y = 9 \):
\[
f(4) = 9
\]

Final Answers for Part 5:
\[
\boxed{(a) 1, (b) 4, (c) 25, (d) 9}
\]

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Final Summary of All Answers:

1. \(\boxed{(a) -3, (b) 12, (c) \frac{4}{5}, (d) -3}\)
2. \(\boxed{(a) -4, (b) 12, (c) -3, (d) 0.8}\)
3. \(\boxed{(a) 5, (b) \frac{1}{2}, (c) 0, (d) 3}\)
4. \(\boxed{(a) 9, (b) -1, (c) 0, (d) 5}\)
5. \(\boxed{(a) 1, (b) 4, (c) 25, (d) 9}\)