Key Features of Square & Cube Root Functions

Front

What is a Cube Root Function?

Back

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

Front

What is the Range of all Cube Root Functions?

Back

(−∞, ∞)

Front

What is the general form of a Square Root Function?

Back

A function of the form f(x) = √(x - h) + k, where (h, k) is the vertex.

Front

What is the domain of a Square Root Function?

Back

The domain is [h, ∞) where h is the x-value that makes the expression under the square root non-negative.

Front

How does the graph of a Cube Root Function behave as x approaches infinity?

Back

As x approaches infinity, f(x) also approaches infinity.

Front

What is the y-intercept of the function y = √(x - 5) + 4?

Back

The y-intercept is (5, 4).

Front

What transformation does the equation y = √(x + 1) represent?

Back

A horizontal shift to the left by 1 unit.

Front

What is the effect of a negative sign in front of a Square Root Function?

Back

It reflects the graph across the x-axis.

Front

What is the y-intercept of the function y = -√(x) + 1?

Back

The y-intercept is (0, 1).

Front

What is the difference between a Cube Root Function and a Cubic Function?

Back

A Cube Root Function has the form f(x) = ∛x, while a Cubic Function has the form f(x) = x³.