Problem: Evaluate each function at the specified value.
We are given a series of functions and specific values of \( x \). We need to substitute the given \( x \)-values into each function and compute the result. Let's solve each problem step by step.
---
1) \( f(x) = 3x + 15 \); \( x = 9 \)
Substitute \( x = 9 \) into the function:
\[
f(9) = 3(9) + 15
\]
Calculate:
\[
f(9) = 27 + 15 = 42
\]
Answer:
\[
\boxed{42}
\]
---
2) \( f(x) = 2x^2 - 11 \); \( x = -5 \)
Substitute \( x = -5 \) into the function:
\[
f(-5) = 2(-5)^2 - 11
\]
Calculate \( (-5)^2 \):
\[
(-5)^2 = 25
\]
Now substitute back:
\[
f(-5) = 2(25) - 11
\]
Calculate:
\[
f(-5) = 50 - 11 = 39
\]
Answer:
\[
\boxed{39}
\]
---
3) \( f(x) = -x^3 + 13x \); \( x = -2 \)
Substitute \( x = -2 \) into the function:
\[
f(-2) = -(-2)^3 + 13(-2)
\]
Calculate \( (-2)^3 \):
\[
(-2)^3 = -8
\]
Now substitute back:
\[
f(-2) = -(-8) + 13(-2)
\]
Simplify:
\[
f(-2) = 8 - 26 = -18
\]
Answer:
\[
\boxed{-18}
\]
---
4) \( f(x) = 7x - 13 \); \( x = -6 \)
Substitute \( x = -6 \) into the function:
\[
f(-6) = 7(-6) - 13
\]
Calculate:
\[
f(-6) = -42 - 13 = -55
\]
Answer:
\[
\boxed{-55}
\]
---
5) \( f(x) = 4x^2 - 7x \); \( x = 6 \)
Substitute \( x = 6 \) into the function:
\[
f(6) = 4(6)^2 - 7(6)
\]
Calculate \( (6)^2 \):
\[
(6)^2 = 36
\]
Now substitute back:
\[
f(6) = 4(36) - 7(6)
\]
Calculate:
\[
f(6) = 144 - 42 = 102
\]
Answer:
\[
\boxed{102}
\]
---
6) \( f(x) = 5x^2 - 8x^2 \); \( x = 3 \)
First, simplify the function:
\[
f(x) = 5x^2 - 8x^2 = -3x^2
\]
Now substitute \( x = 3 \) into the simplified function:
\[
f(3) = -3(3)^2
\]
Calculate \( (3)^2 \):
\[
(3)^2 = 9
\]
Now substitute back:
\[
f(3) = -3(9) = -27
\]
Answer:
\[
\boxed{-27}
\]
---
7) \( f(x) = -2x \); \( x = 4 \)
Substitute \( x = 4 \) into the function:
\[
f(4) = -2(4)
\]
Calculate:
\[
f(4) = -8
\]
Answer:
\[
\boxed{-8}
\]
---
8) \( f(x) = x^2 - x + 10 \); \( x = -9 \)
Substitute \( x = -9 \) into the function:
\[
f(-9) = (-9)^2 - (-9) + 10
\]
Calculate \( (-9)^2 \):
\[
(-9)^2 = 81
\]
Now substitute back:
\[
f(-9) = 81 - (-9) + 10
\]
Simplify:
\[
f(-9) = 81 + 9 + 10 = 100
\]
Answer:
\[
\boxed{100}
\]
---
9) \( f(x) = -x^2 + 8 \); \( x = 7 \)
Substitute \( x = 7 \) into the function:
\[
f(7) = -(7)^2 + 8
\]
Calculate \( (7)^2 \):
\[
(7)^2 = 49
\]
Now substitute back:
\[
f(7) = -49 + 8 = -41
\]
Answer:
\[
\boxed{-41}
\]
---
10) \( f(x) = 9x + 12 \); \( x = 1 \)
Substitute \( x = 1 \) into the function:
\[
f(1) = 9(1) + 12
\]
Calculate:
\[
f(1) = 9 + 12 = 21
\]
Answer:
\[
\boxed{21}
\]
---
Final Answers:
\[
\boxed{42, 39, -18, -55, 102, -27, -8, 100, -41, 21}
\]
Parent Tip: Review the logic above to help your child master the concept of function worksheets.
