Suppose f(x) = x^2 What is the graph of g(x)= 1/4 f(x)?

Answer with explanation:

We are given a function f(x) in terms of variable x as:

We know that a transformation of a parent function f(x) of the type:

         f(x) → a f(x)

is either a vertical stretch or a shrink depending on a.

If a>1 then the transformation is a vertical stretch and if a<1 then it is a vertical squeeze.

Also, the transformation of the type:

      f(x) → f(ax)

  is a horizontal stretch if a<1 and a horizontal shrink if a>1.

Here we have:

This means that the function g(x) is a vertical shrink of the parent function f(x) since a=1/2 <1

Also, we can represent our function as:

This means that:

Here we have: a=1/√2 <1

This means that it is a horizontal stretch.

step-by-step explanation: