# Graph f(2x) with a Simple f(x) Equation

• wScott

## Homework Statement

Given f(x) = x^2. Graph f(2x)

## Homework Equations

I just need to draw the graph

## The Attempt at a Solution

What I tried was putting the x value in the equation which would give me the y value by means of the x^2 part, and the x value would double to give me my new point. This wasn't what the answer key had. Any tips?

When you are asked to find f(2x), you need to substitute 2x as a whole for the original x. Will the value of f(x) really double?

it becomes f(2x) = (2x)^2

There are two ways to do this. The simplest is to do what theperthvan (and, indirectly, Tedjn) suggests: replace x by 2x. What is (2x)2?

The other is to argue that any change before the "main" function, x2, is applied is a change in x and so changes the graph only horizontally. The value x= 1, after multiplying by 2, becomes the same as x= 2. But 1 is only 1/2 as far from the origin as 2: the whole graph of y= x2 is "squeezed" by 1/2 horizontally but not changed vertically.