If we want to make the graph wider, then we must have a horizontal dilation, so the correct option will be 1/4.
How do horizontal dilations work?
A horizontal dilation is a transformation that makes the graph of a function wider.
For a function f(x) an horizontal dilation of scale factor k (with k > 1) is written as:
g(x) = f(x/k)
For the case of the absolute value function we will have:
g(x) = |x/k| = (1/k)*|x|
So we need to find the value (1/k).
Remenber that k > 1, then 0 < (1/k) < 1.
This means that the only values between 0 and 1 could fill the blank in such a way that the graph of that function is wider than the one of the parent function, so from the given options, we will take:
1/k = 1/4
Then the function is:
g(x) = (1/4)*|x|
This function will have a graph wider than the one of f(x) = |x|
If you want to learn more about transformations, you can read:
https://brainly.com/question/17586310
