Question

Given the parent function of f(x) = x4, what change will occur when the function is changed to f, bracket one half x end bracket?

A. Graph opens the same way and is narrower.
B. Graph opens the same way and is wider.
C. Graph opens the opposite way and is narrower.
D. Graph opens the opposite way and is wider.

Answer 1

The choice is 1. For it to be opposite, has to be negative, which is not the case here. It is narrower cuz it's half.

Answer 2

B. Graph opens the same way and is wider

Explanation:

We have
`f(x) = x^(4)`

Now, the function g(x) is made by changing f(x) to f(x/2),

i.e.
`g(x) = f((x)/(2) )`.

i.e.
`g(x) =( (x)/(2) )^(4)`

i.e.
`g(x) = (x^(4) )/(16)`.

So, we plot both the functions
`f(x) = x^(4)` and
`g(x) = (x^(4) )/(16)`.

Hence, option B is correct from the graph below.