Cube and Cube Root Functions

Front

What is a cube function?

Back

A cube function is a polynomial function of the form f(x) = x^3, where the variable x is raised to the power of 3.

Front

What is a cube root function?

Back

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

Front

What is the domain of all cube root functions?

Back

The domain of all cube root functions is (−∞, ∞), meaning they are defined for all real numbers.

Front

What is the range of cube functions?

Back

The range of cube functions is also (−∞, ∞), as they can produce all real numbers.

Front

How does the graph of f(x) = x^3 behave?

Back

The graph of f(x) = x^3 passes through the origin (0,0) and increases steeply in both the positive and negative directions.

Front

What effect does adding a constant have on the graph of a cube function?

Back

Adding a constant shifts the graph vertically. For example, f(x) = x^3 + 2 shifts the graph up by 2 units.

Front

What effect does subtracting a constant have on the graph of a cube root function?

Back

Subtracting a constant shifts the graph vertically down. For example, f(x) = ∛x - 1 shifts the graph down by 1 unit.

Front

What is the inverse of a cube function?

Back

The inverse of a cube function f(x) = x^3 is the cube root function f^{-1}(x) = ∛x.

Front

What is the general form of a transformed cube root function?

Back

The general form is f(x) = a∛(x - h) + k, where (h, k) is the translation and 'a' affects the vertical stretch or compression.

Front

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

Back

Look for the values of h and k in f(x) = a∛(x - h) + k. 'h' indicates horizontal shifts, and 'k' indicates vertical shifts.