Linear Transformations

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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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What effect does adding a constant to a function have on its graph?

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Adding a constant to a function results in a vertical shift of the graph. If the constant is positive, the graph shifts up; if negative, it shifts down.

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What is the effect of multiplying a function by a constant greater than 1?

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Multiplying a function by a constant greater than 1 results in a vertical stretch of the graph.

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What is the effect of multiplying a function by a constant between 0 and 1?

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Multiplying a function by a constant between 0 and 1 results in a vertical compression of the graph.

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