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Function Transformation

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Horizontal Stretch

Increases the distance between points along the x-axis, effectively stretching the graph horizontally.

Horizontal Compression

Decreases the distance between points along the x-axis, compressing the graph horizontally.

Vertical Stretch

Increases the distance between points along the y-axis, stretching the graph vertically.

Vertical Compression

Decreases the distance between points along the y-axis, compressing the graph vertically.

Reflection over the x-axis

Flips the graph over the x-axis.

Reflection over the y-axis

Flips the graph over the y-axis.

Horizontal Translation

Shifts the graph horizontally to the left or right.

Vertical Translation

Shifts the graph vertically up or down.

Reflection over the line $y = x$

Flips the graph over the line $y = x$ , interchanging the roles of $x$ and $y$ .

Rotation by 90 degrees clockwise

Rotates the graph 90 degrees in a clockwise direction around the origin.

Rotation by 90 degrees counterclockwise

Rotates the graph 90 degrees in a counterclockwise direction around the origin.

Scaling

Multiplies both x and y-coordinates of the original function by constant factors to scale the graph.

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