Radical Functions

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What is a radical function?

Back

A radical function is a function that contains a variable within a radical, such as a square root, cube root, etc. The most common form is @@f(x) = oot{n}{x}@@.

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What is the parent function of a square root function?

Back

The parent function of a square root function is @@f(x) = oot{2}{x}@@, which has a starting point at (0,0) and is defined for x >= 0.

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What does a vertical stretch by a factor of 'a' do to the graph of a function?

Back

A vertical stretch by a factor of 'a' (where a > 1) multiplies the output values of the function by 'a', making the graph taller.

Front

What does a vertical compression by a factor of 'b' do to the graph of a function?

Back

A vertical compression by a factor of 'b' (where 0 < b < 1) multiplies the output values of the function by 'b', making the graph shorter.

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Front

How do you identify the transformations of the function @@f(x) = a oot{2}{x - h} + k@@?

Back

The transformations are: vertical stretch/compression by |a|, horizontal shift right by h, and vertical shift up by k.

Front

What is the effect of a negative 'a' in the function @@f(x) = -a oot{2}{x}@@?

Back

A negative 'a' reflects the graph over the x-axis.