Transformations Of Graphs Worksheet

Transformations of graphs at a glance

Graph transformations are transformations that can be applied to graphs of functions. In GCSE maths, we study reflections and translations of graphs. Transforming a graph affects the equation of the graph in a specific way that we need to learn. If we start with the graph with equation y=f(x), then:

y=f(x)+a is a translation of a units in the y direction (vertical translation)

y=f(x+a) ia a translation of -a in the x direction (horizontal translation)

y=-f(x) is a reflection in the x axis

y=f(-x) is a reflection in the y axis

In GCSE maths, you may be asked to sketch a graph after identifying the transformation from the equation, or to write the equation after identifying the transformation. You may also be asked to write down the new coordinates of a certain point on the graph, for example the new coordinates of the minimum point or maximum point (also called the turning points) of the graph. 

Graph transformations are studied further in A Level maths and enlargements of graphs (called stretches) are introduced.

Looking forward, students can then progress to additional interpreting graphs worksheets and other algebra worksheets, for example a sequences worksheet, simultaneous equations worksheet or straight line graphs worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.