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?

 

[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?

 

[theperthvan]

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

 

[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.