In this series of activities, we will be tying two topics together, transforming a graph that is given both in** function notation [f(x)]** and **cartesian [y = ]**.

**How to transform graphs**

When studying shapes, you will have become familiar with the four different types of transformation - reflection, rotation, translation and enlargement.

When you are dealing with transforming graphs, you can **translate**, **reflect **and **stretch**, enlarging in one direction, but not rotation.

In this activity, we are going to look at **stretching vertically**.

**y = f(x) → y = af(x)**

This does like quite daunting at first but it is actually quite intuitive.

f(x) just describes any function - it could be a quadratic, a linear graph, a circle or any other function. For example, here is a random function:

If we apply the transformation y = af(x), we are multiplying every value of the function by **a** (which could be any value) **after** we have evaluated the function. This means that the value of **y** will be **a** times larger than in the original function. This will make the graph** stretch in a vertical direction** with a scale factor of **a.**

The function** y = af(x) is a stretch in a vertical direction with a scale factor of a.**

**How to apply this to a graph**

**Example:**

You are given the function y = x^{2} - 4

**Sketch the graph of y = 2(x ^{2} – 4)**

In the transformation **y = af(x), a = 2 **so every value of y will double and the values of x will stay the same.

Sometimes when you translate a function, you will be expected to label the significant points that have been translated.

This only needs to be done if it is specifically asked for.

Let's try some questions now.