Transforming graphs of functions is something that can be done in Math. Where we already have the graph of a function, but can apply operations to the function in order to change the location or shape of the graph.

This page will show examples of transformations that can be done to a quadratic graph, and the operations that create them.

The quadratic graph we’ll use is a standard curve shown below, but the transformations shown on this page do also apply to other quadratic graphs that can be encountered.

## Transforming Graphs Examples

1)     y = \space {\text{-}}f(x)

Reflect the graph in the  x-axis.

2)     y = \space f({\text{-}}x)

Reflect the graph in the  y-axis.

3)     y = \space {\text{-}}f({\text{-}}x)

Reflect the graph in the  y-axis, then the  x-axis.

4)     y = \space f(x) + 1

Move the graph up the  x-axis  1 unit.

5)     y = \space f(x + 1)

Move the graph along the  y-axis  1 unit left.

6)     y = \space f(\frac{x}{2})

Stretch the graph by 2 in the  x  direction.

7)     y = \space 2f(x)

Stretch the graph by 2 in the  y  direction.

8)     y = \space 2 \space {\text{--}} \space f(x)

Reflect the graph in the  x-axis,  then move up by 2 units.

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