Question

Help!

Answer 1

With what?

Answer 2

Choose the characteristics of the function: f(x) = 2(x - 4)^5
A. The left end goes up and the right end goes down
B. Both ends go up
C. Its parent function was flipped and translated right
D. Its parent function was stretched and translated right
E. There are 5 roots and at most 4 relative extrema
F. There are 4 roots and at most 5 relative extrema

Answer 3

I know nothing about parent function or relative extremas but here is a graph of the function so perhaps it'll help?

Answer 4

Clearly A is incorrect and as far as I can tell there is only one root...

Answer 5

Which others do you think are not correct?

Answer 6

Aha! googled it and a parent function is " the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form

y = ax^2 + bx + c

the simplest function is

y = x^2."

Which makes it clear that the parent function is x^5 in this case.

The graph below shows that the parent function was definitely translated right. Something less obvious from the graph is the fact that the function was stretched but referring back to our knowledge of function: multiplying x by a number stretches x by a factor of that number (something like that). which makes it clear that the graph was stretched.

Note also that when you ADD a number to x in a function you move the graph of the function in the Negative x-direction and vice versa so from that alone we know the graph was translated right.

Answer 7

Oooohhhh the relative extrema are just the maximums and minimums of the graph! it is clear there are only one or two of those so I think the only right one is C.