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
