Square Root Functions - Key Features, Transformations, Inverses

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What is a square root function?

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CCSS.HSF.IF.A.2

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The domain of the square root function is [0, ∞) because the square root of a negative number is not defined in the set of real numbers.

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The range of the square root function is [0, ∞) because the output of the square root function is always non-negative.

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How do you find the inverse of a function?

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To find the inverse of a function, swap the x and y variables and solve for y.

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CCSS.HSF-BF.B.4A

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CCSS.HSF-BF.B.4A

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What does it mean for a function to be one-to-one?

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A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once.

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CCSS.HSF.BF.B.3

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What is the reflection property of a function and its inverse?

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The graph of a function and its inverse are reflections of each other over the line y = x.

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CCSS.HSF-BF.B.4B

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What is the significance of the point (a, b) on a function?

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If (a, b) is a point on the function f(x), then (b, a) will be a point on the inverse function f^-1(x).

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CCSS.HSF-BF.B.4C

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CCSS.HSF-BF.B.4A