1. Maths Transforming Graphs
GCSE Revision 101
Maths
Transforming Graphs
© Daniel Holloway

2. The Basics
Transforming graphs is not too dissimilar from transforming shapes. Whereas you can translate, rotate, reflect and enlarge shapes; you can translate, stretch and reflect graphs. We use the notation f(x) to denote a function of x. A function of x is any algebraic expression where x is the only variable.

3. The Basics
There are six rules you need to learn about transforming graphs. To show these rules, we will use the following graph. This is the graph y = f(x)

4. Translating Graphs y = f(x) + a
Rule 1: This is a translation of the graph in the vector ( ) in the y-direction a
y = f(x) + a

5. Translating Graphs y = f(x – a)
Rule 2: This is a translation of the graph in the vector ( ) in the x-direction a
y = f(x – a)

6. Stretching Graphs y = kf(x)
Rule 3: This is a stretch of the graph by a scale factor of k in the y-direction Note that they cross at the x axis
y = kf(x)

7. Stretching Graphs y = f(tx)
Rule 4: This is a stretch of the graph by a scale factor of 1/t in the x-direction Note that they cross at the y axis
y = f(tx)

8. Reflecting Graphs y = -f(x)
Rule 5: This is a reflection of the graph in the x-axis
y = -f(x)

9. Reflecting Graphs y = f(-x)
Rule 6: This is a reflection of the graph in the y-axis
y = f(-x)

10. Examples of Transformationsy y 5 5 -5 5 x -5 5 x
The grid shows the graph of y=x2 for -2 ≤ x ≤ 2
The dotted line shows the same graph. Describe the transformation taking it to the new line on the grid.
y = (x + 3) 2

11. Examples of Transformationsy y 5 5 -5 5 x -5 5 x
The grid shows the graph of y=x2 for -2 ≤ x ≤ 2
The dotted line shows the same graph. Describe the transformation taking it to the new line on the grid.
y = x2 - 2

12. Examples of Transformationsy y 5 5 -5 5 x -5 5 x
The grid shows the graph of y=x2 for -2 ≤ x ≤ 2
The dotted line shows the same graph. Describe the transformation taking it to the new line on the grid.
y = 2x2