Question

Given the parent function of f(x) = x^4, what change will occur when the function is changed to -f(1/2x) ?

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

Answer: D. Graph opens the opposite way and is wider.

Step-by-step explanation:

Let
`y=f(x).`.

Then, the given equations are:

`y=x^(2)`

and

`y=-(1)/(16)x^4.`.

The graph for both the curves are attached. From there, we can easily check that the new function
`-f(1/2x)` will have graph in the opposite way to the parent one
`f(x)` and also wider than that.

Hence, the correct option is D. Graph opens the opposite way and is wider.

Answer 2

we are given with a function equal to f(x) = x^4. When the function is changed to -f(1/2x), the function changes to -f(1/2x) = (1/2 x)^4 equal to (-1/16 x^4). The graph of the function should be opening the opposite way and has  a narrower plot. answer is C