Here is the step-by-step solution to all parts of the worksheet:
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A) Evaluate each function at the specified value.
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1) f(x) = 9^(3x - 10), x = 10
Substitute x = 10 into the function:
f(10) = 9^(3*10 - 10)
= 9^(30 - 10)
= 9^20
This is a very large number, but we can leave it as
9²⁰ unless asked for decimal form.
✔ Answer: 9²⁰
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2) f(x) = 8 · (-2)^(x - 1) - 3, x = 2
Substitute x = 2:
f(2) = 8 · (-2)^(2 - 1) - 3
= 8 · (-2)^1 - 3
= 8 · (-2) - 3
= -16 - 3
=
-19
✔ Answer: -19
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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.
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1) If f(x) = 10 · 4^x - 11, find f(-2).
Substitute x = -2:
f(-2) = 10 · 4^(-2) - 11
= 10 · (1/4²) - 11
= 10 · (1/16) - 11
= 10/16 - 11
= 5/8 - 11
= 5/8 - 88/8
=
-83/8 or
-10.375
✔ Answer: -83/8 (or -10.375)
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2) If f(x) = 4^(x - 2) + 1, find f(3).
Substitute x = 3:
f(3) = 4^(3 - 2) + 1
= 4^1 + 1
= 4 + 1
=
5
✔ Answer: 5
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3) If f(x) = 13 · (-5)^(9 + x), find f(-8).
Substitute x = -8:
f(-8) = 13 · (-5)^(9 + (-8))
= 13 · (-5)^1
= 13 · (-5)
=
-65
✔ Answer: -65
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4) If f(x) = -7 + (-1)^(x - 1), find f(-5).
Substitute x = -5:
f(-5) = -7 + (-1)^(-5 - 1)
= -7 + (-1)^(-6)
= -7 + [1 / (-1)^6]
= -7 + [1 / 1]
= -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 + 0
=
36
✔ Answer: i) 36
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✔ Final Answers Summary:
A)
1) 9²⁰
2) -19
3) 37
4) -101
B)
1) -83/8
2) 5
3) -65
4) -6
C)
i) 36
Let me know if you’d like any part explained further!
Parent Tip: Review the logic above to help your child master the concept of practice worksheet exponential functions.
