Transformations of Square and Cube Root Functions

Front

What is a square root function?

Back

A function of the form f(x) = √x, which represents the principal square root of x.

Front

What is a cube root function?

Back

A function of the form f(x) = ∛x, which represents the principal cube root of x.

Front

What does it mean to translate a function?

Back

To shift the graph of the function horizontally or vertically without changing its shape.

Front

How does a translation to the right affect the function f(x)?

Back

The function f(x) is replaced by f(x - h), where h is the number of units shifted right.

Front

How does a translation to the left affect the function f(x)?

Back

The function f(x) is replaced by f(x + h), where h is the number of units shifted left.

Front

What does a vertical shift of a function entail?

Back

Adding or subtracting a constant from the function, resulting in a shift up or down.

Front

What is the effect of reflecting a function over the x-axis?

Back

The function f(x) is replaced by -f(x), flipping it vertically.

Front

What is the domain of all square root functions?

Back

The domain is [0, ∞), as square roots of negative numbers are not real.

Front

What is the range of all square root functions?

Back

The range is [0, ∞), as square root values are non-negative.

Front

What is the domain of all cube root functions?

Back

The domain is (−∞, ∞), as cube roots are defined for all real numbers.