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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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).

Tags

CCSS.HSF.BF.B.3

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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, (-∞, ∞).

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B