GCSE 9-1 maths: Functions, Shifts (translate), Stretches, Scale factors, Reflections

Instead of being specific with an equation (e.g. y = x^{2}, i.e. get y values from x squared values) we may write y = f(x).

This means that y is connected to x in some way, but it's unknown. Its called function notation and if you draw a wiggly line curve you can just say it's a graph of y=f(x).

The wiggly line curve of a functions can be shifted up and down, left or right and can be enlarged or squashed in the horizontal or vertical directions.

**Q**. What has happened to the graph of the function below:

ANS

The graph of a functions can be transformed (changed) in several ways. Basically this means **moving or enlarging or refecting** the graph.

You can transform a graph by moving the whole graph up or down in the y-direction or the x-direction. This is called a shift or better say, **Translate**.

You can also transform a graph by enlarging or squashing it, again in the y-direction or the x-direction. The amount of enlargement comes from the scale factor (SF) used.

This is called a **Stretch** (even though sometimes it is a squash)

Finally you can **Reflect** graphs using the x or y axis as your mirror line.

When asked to describe how a graph is transformed, say **how it was changed** and in **which direction** it happened.

When you place values inside the brackets it affects the x-direction onf the graph.

A positive (+1) value shifts the graph in the negative x-direction

and a negative value (– shifts the graph in the positive x-direction.

The graph of y = f(x) is shown on the grid.

Sketch the graph of y = f(x – 1)

When you place values inside the brackets it affects the x-direction of the graph.

This time instead of multiplying by a scale factors, we **divide by the scale factor.**

So y= f(x) → y = f(3x) will have the affect of dividing all x values by 3.

The graph of y = f(x) is shown on the grid.

Sketch the graph of y = f(2x)

(Hint: for every value of old x, just divide by 2 to get the new x value and plot)