In this deck, we'll explore graph transformations. This is about taking a standard graph, represented by the equation y equals f of x, and changing its equation to see how the graph moves or changes shape. We'll cover three main types of transformation: translations, which are slides; stretches; and reflections.

Let's start with translations. Imagine we change our equation from y equals f of x to y equals f of x plus a, where the number 'a' is added on the outside of the function. This change affects the y-values directly. If 'a' is a positive number, all the y-coordinates increase, and the whole graph slides straight up. If 'a' is a negative number, the graph slides straight down.

Now let's look at what happens when we change the input to the function. This means the change happens inside the brackets, like y equals f of, open bracket, x plus a, close bracket. This affects the x-coordinates, causing a horizontal slide. But be careful, it works in the opposite way to what you might expect. Adding a positive number inside the brackets actually moves the graph to the left, in the negative direction.