Transformations of Functions

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What is a transformation of a function?

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A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

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What does a vertical shift of a function do?

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A vertical shift moves the graph of the function up or down without changing its shape.

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What is the effect of a horizontal shift on a function?

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A horizontal shift moves the graph of the function left or right, affecting the x-coordinates of the points on the graph.

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What does reflecting a function over the x-axis do?

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Reflecting a function over the x-axis changes the sign of the output values (y-values), resulting in an upside-down version of the graph.

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What does reflecting a function over the y-axis do?

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Reflecting a function over the y-axis changes the sign of the input values (x-values), resulting in a mirror image of the graph across the y-axis.

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How does a vertical stretch affect a function?

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A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

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How does a vertical compression affect a function?

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A vertical compression decreases the distance between points on the graph and the x-axis, making the graph shorter.

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