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.