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