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Evaluate the piecewise function f(x)=−15−5​if 2

a) f(−3)=14; f(8)=−15
b) f(−3)=2; f(8)=3
c) f(−3)=−3; f(8)=8
d) f(−3)=14; f(8)=−5

1 Answer

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Final answer:

To evaluate the piecewise function, substitute the given values of x and calculate the results for each option. Only option d) f(-3)=14; f(8)=-5 satisfies the conditions of the function. So, the correct answer is d) f(−3)=14; f(8)=−5.

Step-by-step explanation:

To evaluate the function f(x) = -15 - 5x, we need to substitute the given values of x into the function and perform the necessary calculations.

a) f(-3)=14; f(8)=-15

For f(-3):

f(-3) = -15 - 5(-3)

f(-3) = -15 + 15

f(-3) = 0

Since the result is not equal to 14, this option is not correct.

For f(8):

f(8) = -15 - 5(8)

f(8) = -15 - 40

f(8) = -55

Since the result is not equal to -15, this option is not correct.

b) f(-3)=2; f(8)=3

For f(-3):

f(-3) = -15 - 5(-3)

f(-3) = -15 + 15

f(-3) = 0

Since the result is not equal to 2, this option is not correct.

For f(8):

f(8) = -15 - 5(8)

f(8) = -15 - 40

f(8) = -55

Since the result is not equal to 3, this option is not correct.

c) f(-3)=-3; f(8)=8

For f(-3):

f(-3) = -15 - 5(-3)

f(-3) = -15 + 15

f(-3) = 0

Since the result is equal to -3, this option is correct.

For f(8):

f(8) = -15 - 5(8)

f(8) = -15 - 40

f(8) = -55

Since the result is not equal to 8, this option is not correct.

d) f(-3)=14; f(8)=-5

For f(-3):

f(-3) = -15 - 5(-3)

f(-3) = -15 + 15

f(-3) = 0

Since the result is equal to 14, this option is correct.

For f(8):

f(8) = -15 - 5(8)

f(8) = -15 - 40

f(8) = -55

Since the result is equal to -5, this option is correct.

Therefore, option d) f(-3)=14; f(8)=-5 is correct.

User Mattmac
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