# Simple f(x) equation

1. Feb 27, 2007

### wScott

1. The problem statement, all variables and given/known data
Given f(x) = x^2. Graph f(2x)

2. Relevant equations

I just need to draw the graph

3. 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?

2. Feb 27, 2007

### Tedjn

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?

3. Feb 27, 2007

### theperthvan

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

4. Feb 27, 2007

### HallsofIvy

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.