Flashcard Parent Functions and Transformations

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What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x^2), and absolute value functions (y = |x|).

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Shrinks by a factor of 1/2, shifts right 1 unit, and shifts down 1 unit.

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Absolute value function.

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Vertical shrink by a factor of 4/5, shifts left 5 units, and shifts up 2 units.

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Back

Quadratic function.

Front

What is the general form of a quadratic function?

Back

Front

What is a vertical stretch in transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

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What is a vertical shrink in transformations?

Back

A vertical shrink occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

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What does shifting a graph to the right mean?

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Shifting a graph to the right means adding a positive value to the input variable (x), which moves the graph horizontally.

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What does shifting a graph down mean?

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Shifting a graph down means subtracting a value from the output variable (y), which moves the graph vertically.