Question

Consider the function f(x) = 9x. Which statement MUST be true? A) f(4) f(1) = f(8) f(5) B) f(4)·f(1) = f(8)·f(5) C) f(4) − f(1) = f(8) − f(5) D) f(4) − f(1) = f(−4) − f(−1)

Answer 1

Answer with Step-by-step explanation:

We are given that:

f(x)=9x

A) f(4) f(1) = f(8) f(5)

f(4)f(1)=9×4×9×1=324

f(8)f(5)=9×8×9×5=3240

Hence, this option is incorrect

B) f(4)·f(1) = f(8)·f(5)

f(4)f(1)=324

f(8)f(5)=3240

Hence, this option is incorrect

C) f(4) − f(1) = f(8) − f(5)

f(4)-f(1)=9×4-9=27

f(8) − f(5)=9×8-9×5=27

Hence, this option is correct

D) f(4) − f(1) = f(−4) − f(−1)

f(4) − f(1)=9×4-9=27

f(−4) − f(−1)=9×(-4)+9=-27

Hence, this option is incorrect

Correct option is:

C) f(4) − f(1) = f(8) − f(5)

Answer 2

Answer:

The correct answer is A

Step-by-step explanation:

Exponential functions grow by equal factors over equal intervals because the change in x is always the same as the exponent of the quotient of the values of y.