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 input value 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

What does the parameter 'a' in the cube root function affect?

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 do you find the center point of a cube root function?

Back

The center point (h, k) can be found from the function's equation in the form f(x) = a ∛(x - h) + k.

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 does the graph of a cube root function behave as x approaches infinity?

Back

As x approaches infinity, f(x) approaches infinity, indicating that the graph rises to the right.

Front

How does the graph of a cube root function behave as x approaches negative infinity?

Back

As x approaches negative infinity, f(x) approaches negative infinity, indicating that the graph falls to the left.

Front

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

Back

The graph of a cube root function has a characteristic S-shape, passing through the origin (0,0) when no transformations are applied.

Front

What is the difference between a cube root function and a cubic function?

Back

A cube root function is of the form f(x) = ∛(x), while a cubic function is of the form f(x) = x³, which has a different shape and properties.