A tutorial on graphing and sketching cube root functions is presented. The graph, domain, range of these functions and other properties are discussed.
Example 1: Graph
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:
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.
Example 2: Graph
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 ∛ (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.
The last two rows in the table of data are used to graph f. The range of f is the set of all real numbers. Note also that the graph of f(x) = ∛ (x  2) is that of f(x) = ∛ ( x ) shifted 2 units to the right.
Example 3: Graph
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 .
The range of f is given by the interval (∞ , +∞).
Example 4: Graph
and find the range of f.
Solution to Example 4:
The range of f is the set of all real numbers. More references and links on graphing. Graphing Functions
