Math worksheet for evaluating linear functions, featuring eight problems with different functions and input values.

Sure! Let’s solve each problem step by step. The task is to evaluate linear functions at given values of \( x \). This means we substitute the given \( x \)-value into the function and simplify.

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Problem 1:

Find \( h(-4) \) if \( h(x) = -6x - 4 \)

Substitute \( x = -4 \):

\[
h(-4) = -6(-4) - 4 = 24 - 4 = 20
\]

✔ Answer: \( \boxed{20} \)

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Problem 2:

Find \( h(-10) \) if \( h(x) = 10x - 8 \)

Substitute \( x = -10 \):

\[
h(-10) = 10(-10) - 8 = -100 - 8 = -108
\]

✔ Answer: \( \boxed{-108} \)

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Problem 3:

Find \( h\left(\frac{28}{23}\right) \) if \( h(x) = -10x + 3 \)

Substitute \( x = \frac{28}{23} \):

\[
h\left(\frac{28}{23}\right) = -10 \cdot \frac{28}{23} + 3 = -\frac{280}{23} + 3
\]

Convert 3 to a fraction with denominator 23:

\[
3 = \frac{69}{23}
\]

Now combine:

\[
-\frac{280}{23} + \frac{69}{23} = \frac{-280 + 69}{23} = \frac{-211}{23}
\]

✔ Answer: \( \boxed{-\frac{211}{23}} \) (or as a mixed number: \( -9 \frac{4}{23} \))

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Problem 4:

Find \( h\left(\frac{7}{6}\right) \) if \( h(x) = -4x - 5 \)

Substitute \( x = \frac{7}{6} \):

\[
h\left(\frac{7}{6}\right) = -4 \cdot \frac{7}{6} - 5 = -\frac{28}{6} - 5
\]

Simplify \( \frac{28}{6} = \frac{14}{3} \), so:

\[
-\frac{14}{3} - 5 = -\frac{14}{3} - \frac{15}{3} = -\frac{29}{3}
\]

✔ Answer: \( \boxed{-\frac{29}{3}} \) (or as a mixed number: \( -9 \frac{2}{3} \))

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Problem 5:

Find \( f(-5) \) if \( f(x) = 2 + \frac{x}{5} \)

Substitute \( x = -5 \):

\[
f(-5) = 2 + \frac{-5}{5} = 2 - 1 = 1
\]

✔ Answer: \( \boxed{1} \)

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Problem 6:

Find \( g(5) \) if \( g(x) = 1 - \frac{x}{1} \)

Note: \( \frac{x}{1} = x \), so this simplifies to:

\[
g(x) = 1 - x
\]

Now substitute \( x = 5 \):

\[
g(5) = 1 - 5 = -4
\]

✔ Answer: \( \boxed{-4} \)

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Problem 7:

Find \( f(-4) \) if \( f(x) = -4 + \frac{20}{x} \)

Substitute \( x = -4 \):

\[
f(-4) = -4 + \frac{20}{-4} = -4 - 5 = -9
\]

✔ Answer: \( \boxed{-9} \)

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Problem 8:

Find \( h(-4) \) if \( h(x) = 10 - \frac{24}{x} \)

Substitute \( x = -4 \):

\[
h(-4) = 10 - \frac{24}{-4} = 10 - (-6) = 10 + 6 = 16
\]

✔ Answer: \( \boxed{16} \)

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## ✔ Final Answers Summary:

1. \( \boxed{20} \)
2. \( \boxed{-108} \)
3. \( \boxed{-\frac{211}{23}} \)
4. \( \boxed{-\frac{29}{3}} \)
5. \( \boxed{1} \)
6. \( \boxed{-4} \)
7. \( \boxed{-9} \)
8. \( \boxed{16} \)

Let me know if you’d like to see any steps explained further!