### Transform graphs   More

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

###### Functions

Instead of being specific with an equation (e.g. y = x2, 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

###### 6 ways to transform graphs Menu

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.

###### Shift (Translate) in y-direction Menu

The graph of y = f(x) is shown on the grid.
Sketch the graph of y = f(x) + 1.
(Hint: for every value of old y, just add 1 to get the new y value and plot)

ANS

###### Shift (Translate) in x-direction Menu

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)

ANS

The graph of y = f(x) is shown on the grid.
Sketch the graph of y = 2f(x)
(Hint: for every value of old y, just multiply by 2 to get the new y value and plot)

ANS

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)

ANS

###### Reflections in x or y axis Menu

The graph of y = f(x) is shown on the grid.
Sketch the graph of y = – f(x) and y = f(–x)
(Hint: in first transformation for every old value of y, change its sign)

ANS