2023 -2024 - Graphing Cube Root Functions

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛(x), which returns the number that, when cubed, gives x.

Front

What is the general form of a cube root function?

Back

The general form is f(x) = a ∛(x - h) + k, where (h, k) is the center point of the graph.

Front

How do you find the x-intercept of a cube root function?

Back

To find the x-intercept, set f(x) = 0 and solve for x.

Front

What does the center point of a cube root function represent?

Back

The center point (h, k) represents the point where the graph of the function changes direction.

Front

What effect does the parameter 'a' have in the function f(x) = a ∛(x - h) + k?

Back

The parameter 'a' affects the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

How does the value of 'h' affect the graph of a cube root function?

Back

The value of 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

How does the value of 'k' affect the graph of a cube root function?

Back

The value of 'k' shifts the graph vertically. If k is positive, the graph shifts up; if negative, it shifts down.

Front

What is the domain of a cube root function?

Back

The domain of a cube root function is all real numbers, (-∞, ∞).

Front

What is the range of a cube root function?

Back

The range of a cube root function is also all real numbers, (-∞, ∞).

Front

How do you determine which graph matches a given cube root function?

Back

To determine the matching graph, analyze the transformations based on the values of a, h, and k.