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

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

__1)__Reflect the graph in the x-axis.

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

__2)__Reflect the graph in the y-axis.

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

__3)__Reflect the graph in the y-axis, then the x-axis.

**y = \space f(x) + 1**

__4)__Move the graph up the x-axis 1 unit.

**y = \space f(x + 1)**

__5)__Move the graph along the y-axis 1 unit left.

**y = \space f(\frac{x}{2})**

__6)__Stretch the graph by 2 in the x direction.

**y = \space f({\large{\frac{x}{{\tt{2}}}}})**

__7)__Stretch the graph by 2 in the y direction.

**y = \space 2 \space {\text{–}} \space f(x)**

__8)__Reflect the graph in the x-axis, then move up by 2 units.

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