Linear transformations on Graphs

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What is a linear transformation?

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

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This notation represents a horizontal shift of the function f to the right by c units.

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This notation represents a horizontal shift of the function f to the left by c units.

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This notation represents a vertical shift of the function f upwards by k units.

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This notation represents a vertical shift of the function f downwards by k units.

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This notation represents a vertical stretch or compression of the function f by a factor of a.

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This notation represents a horizontal stretch or compression of the function f by a factor of 1/k.

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The negative sign reflects the graph of the function f across the x-axis.

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The negative sign reflects the graph of the function f across the y-axis.

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The graph of f is shifted to the right by 3 units.