Math Concepts Explained

If you understand how to shift a curve horizontally or vertically, stretching or compressing isn't much different. Once again, it's only a small modification to the equation that causes the stretch or compression.

Stretching or compressing a graph is determined by the coefficient in front of the x (or more specifically, in front of the other direct modifications to x).

Let's look at a basic example.... f(x) = x^2, a standard parabola.


Now, to compress this curve, you put a 'fraction coefficient' in front of the x component of the graph. i.e. f(x)= (1/2)*x^2. This squashes the graph down by a factor of 2. Or, another way to look at it, every y value in this curve is 1/2 of the value in the starting curve. Plot your own points to convince yourself of this. Note that the curve crosses (-2,4) and (2,4) in the original curve, and the new one crosses at (-2,2) and (2,2).

Now, naturally, if you put a whole number coefficient in front of the x term, you will be stretching the graph. For example: f(x) = 2x^2


You can see that this has caused the parabola to stretch upwards. Note that it now crosses (1,2), not (1,1). Or once again, to look at it from a different angle, every y value is now twice the value as in the original graph.

The only other thing that you should keep in mind is that the coefficient to stretch or compress the graph MUST be in front of any brackets that might be surrounding x, and the coefficient will act on any horizontal translation component and the exponent. Convince yourself of this by looking at graphs such as:

f(x) = (x-3)^2....... and f(x)=2(x-3)^2
f(x) = (x+1)^3...... and f(x)=1/2(x+1)^3
f(x) = x + 5...........and f(x) = 4x + 5
f(x) = (x-1)^5 + 7...... and f(x) = 4(x-1)^5 + 7

As you can see, stretching and compressing graphs really aren't that difficult. They are just an extension of what you already know, building on your knowledge of horizontal or vertical shifts. Keep practicing, and you'll get it in no time. :)