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 shape of the graph of a cube root function?

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, resembling a sideways S shape.

Front

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

Back

The graph of f(x) = ∛(x - h) is a horizontal shift of the graph of f(x) = ∛(x) to the right by h units.

Front

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

Back

Adding a constant to a cube root function, such as in f(x) = ∛(x) + k, shifts the graph vertically by k 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, (-∞, ∞), since you can take the cube root of any real number.

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, (-∞, ∞), as the output can be any real number.

Front

How do you identify the transformations of the graph of a cube root function?

Back

Transformations can be identified by looking at the function's equation: horizontal shifts (x - h), vertical shifts (+k), reflections (negative sign), and stretches/compressions.

Front

What is the effect of a negative sign in front of a cube root function, such as in f(x) = -∛(x)?

Back

A negative sign reflects the graph of the cube root function across the x-axis.

Front

How can you determine which graph corresponds to a given cube root function?

Back

To determine the corresponding graph, analyze the function's transformations, such as shifts, reflections, and stretches, and compare them to the options provided.

Front

What is the significance of the point (0,0) on the graph of a cube root function?

Back

The point (0,0) is the origin and is a key point on the graph of a cube root function, indicating that the cube root of 0 is 0.