What are the characteristics of the function fx 2x 45 A Th

What are the characteristics of the function f(x) = 2(x - 4)^5? A. The left end of the graph of the function goes down, and the right end goes up. B. It has 4 zeros and at most 5 relative maximums or minimums. C. It has 5 zeros and at most 4 relative maximums or n D. It is a vertical stretch and a translation to the right of the function. E. It is a reflection and a translation to the right of the participation. F. Both ends of the graph of the function go up.

Solution

f(x) = 2 (x-5)^5
f\'(x) =10*(x-5)^4

we can see that f\'(x) is always greater than 0
so f(x) is always increasing

Hence option A is correct
It can have 5 zeroes and can have maximum of 4 maxima and minima
Hence option C is correct

It is transition to the right and vertically multiplied by 2 with x^5
option D is correct

Answer: A,C,D