Stretches

When we stretch a graph vertically, we are multiplying by a scale factor.

Notice that the graph is stretched in a vertical direction away from the x axis.

If the graph goes below the x axis, where y is negative, it will be stretched down.

If the graph goes above the x axis, where y is positive, it will be stretched up.

See what happens if the scale factor is a number less than 1? What about less than 0?

Now let's look at the maths.

f(x) = 2x - 1

2 f(x) = 2 (2x -1 ) = 4x -2

The gradient of our transformed graph is 4. By stretching with a scale factor of 2, our graph has got steeper.

Notice also that the y intercept is now -2. This has been stretched down, away from the x axis, by the same scale factor.

What would happen if our scale factor is a fraction? Use the graph to investigate.

What would happen if our scale factor is negative?

It's always the horizontal ones that are tricky!

When we think about a horizontal stretch, we need to look BACK to find our values of f(x).

This means that we need to divide our x by the scale factor before calling the function i.e. y= f(x/2). Some people find this difficult, but it's important that you know how it works!

And now let's think about the maths.

We have

f(x) = 2x -1

f(x/2) = 2 (x/2) -1 = x -1

Notice how the gradient has changed. It was 2, and it is now 1. The horizontal stretch has made the line less steep. Makes sense!

The y intercept has stayed the same.