Question

what are the characteristics of the function f(x)=2(x-4)^5

Answer 1

The characteristics are:

A. the left end of the graph of the function goes down, and the right end goes up (like every polynomial of fifth degree that is not reflected)

B. It has 5 zeros and at most 4 relative maximums or minimums (like every polynomial of fifth degree)

D. It is a vertical stretch and a translation to the right of the parent function

The parent function is:

$f(x)=x^5$

the vertical stretch is obtained with the 2 multiplying the parent function. The translation to the right is obtained with the 4 subtracting the variable x.