# Graphing Cube Root Functions

A tutorial on graphing and sketching cube root functions is presented. The graph, domain, range of these functions and other properties are discussed.

The domain of function f defined by f(x) = 3√ ( x ) is the set of all real numbers.

The range of f is the set of all real numbers.

Example 1: Graph

f( x ) = 3√ (x)

and find the range of f.

Solution to Example 1:

Because the domain of f is the set of all real numbers, we might construct a table of values as follows:

 x -8 1 0 1 8 f(x) = 3√ ( x ) -2 1 0 1 2

The values of x were selected so that the cube root of these values are whole numbers which make it easy to plot the points shown in the table.

The range of f is given by the interval (-infinity , +infinity).

Example 2: Graph

f( x ) = 3√ (x - 2)

and find the range of f.

Solution to Example 2:

The domain of the cube root function given above is the set of all real numbers.

It easy to calculate 3√ (x - 2)if you select values of (x - 2) as -8, -1, 0, 1 and 8 to construct a table of values then find x in order to graph f.

 x - 2 -8 -1 0 1 8 f(x) = 3√ (x - 2) -2 -1 0 1 2 x -6 1 2 3 10

Only the last two lines in the table are used to graph f.

The range of f is the set of all real numbers.

Note also that the graph of f(x) = 3√ (x - 2) is that of f(x) = 3√ ( x ) shifted 2 units to the right.

Example 3: Graph

f( x ) = - 3√(x + 1)

and find the range of f.

Solution to Example 3:

The domain of the function given above is the set of all real numbers

We now select values of (x + 1) as -8, -1, 0, 1 and 8 to construct a table of values then find x in order to graph f .

 x + 1 -8 -1 0 1 8 f(x) = - 3√ (x + 1) 2 1 0 - 1 - 2 x -9 -2 -1 0 7

The range of f is given by the interval (-infinity , +infinity).

Example 4: Graph

f( x ) = - 2 3√ (x - 2) + 2

and find the range of f.

Solution to Example 4:

The domain of function f is the set of all real values.

We now select values of (x - 2) as -8, -1, 0, 1 and 8 to construct a table of values.

 x - 2 -8 -1 0 1 8 f(x) = - 2 3√ (x - 2) + 2 6 4 2 0 - 2 x -6 1 2 3 10

The range of f is the set of all real numbers.

More references and links on graphing. Graphing Functions