Linear Transformations

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What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

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Back

This transformation shifts the graph of the function f(x) upward by 3 units.

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Back

This transformation shifts the graph of the function f(x) downward by 3 units.

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This transformation stretches the graph of the function f(x) vertically by a factor of 3.

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Back

This transformation compresses the graph of the function f(x) vertically by a factor of 4.

Front

What does dilating a graph by a factor of -3 mean?

Back

It means to stretch the graph away from the origin by a factor of 3 and reflect it across the x-axis.

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Back

This transformation shifts the graph of the function f(x) upward by 6 units.

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This transformation shifts the graph of the function f(x) downward by 6 units.

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Back

This transformation stretches the graph of the function f(x) vertically by a factor of 6.

Front

What is the difference between a vertical stretch and a vertical compression?

Back

A vertical stretch increases the distance of points from the x-axis, while a vertical compression decreases it.