10-2a-HW-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

How does the graph of a cube root function behave?

Back

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

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 the graph of a cube root function?

Back

Look for a graph that has a horizontal inflection point at the origin and extends into both the first and third quadrants.

Front

What is the effect of a vertical stretch on the cube root function?

Back

A vertical stretch of the cube root function f(x) = ∛x can be represented as f(x) = a∛x, where a > 1 makes the graph steeper.

Front

What is the effect of a vertical compression on the cube root function?

Back

A vertical compression of the cube root function f(x) = ∛x can be represented as f(x) = a∛x, where 0 < a < 1 makes the graph flatter.

Front

What happens to the graph of a cube root function when you add a constant?

Back

Adding a constant c to the function, f(x) = ∛x + c, shifts the graph vertically by c units.

Front

What happens to the graph of a cube root function when you subtract a constant?

Back

Subtracting a constant c from the function, f(x) = ∛x - c, shifts the graph vertically down by c units.

Front

What is the effect of a horizontal shift on the cube root function?

Back

A horizontal shift can be represented as f(x) = ∛(x - h), shifting the graph h units to the right.