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 the original number x.

Front

What is the general shape of the graph of a cube root function?

Back

The graph of a cube root function is a curve that starts from the origin (0,0) and extends into the first and third quadrants, increasing gradually.

Front

How does the graph of f(x) = ∛(x) differ from f(x) = -∛(x)?

Back

The graph of f(x) = -∛(x) is a reflection of f(x) = ∛(x) across the x-axis.

Front

What effect does adding a constant to a cube root function have on its graph?

Back

Adding a constant shifts the graph vertically. For example, f(x) = ∛(x) + 2 shifts the graph up by 2 units.

Front

What is the domain of the cube root function f(x) = ∛(x)?

Back

The domain of f(x) = ∛(x) is all real numbers, (-∞, ∞).

Front

What is the range of the cube root function f(x) = ∛(x)?

Back

The range of f(x) = ∛(x) is also all real numbers, (-∞, ∞).

Front

How do you identify a cube root function from its equation?

Back

A cube root function can be identified by the presence of the cube root symbol (∛) in the equation.

Front

What is the transformation of the function f(x) = ∛(x - 3)?

Back

The function f(x) = ∛(x - 3) represents a horizontal shift of the graph 3 units to the right.

Front

What does the negative sign in f(x) = -∛(x + 3) indicate about the graph?

Back

The negative sign indicates that the graph is reflected across the x-axis.

Front

How can you determine the intercepts of a cube root function?

Back

To find the x-intercept, set f(x) = 0 and solve for x. The y-intercept is found by evaluating f(0).