
Functions and Graphs 2-21
Solution:
a. Given f(x) = x
2
. x-intercept is (0, 0) and so is the y-intercept.
Let us choose and tabulate a few points:
x
y = x
2
-4
16
-2
4
0 0
2 4
4 16
Plotting these points yields the required graph as below:
-4 -2 2 4
4
2
-2
-4
Figure 2.17
Since the graph extends forever both in the positive and negative x direction, the domain of f is {all real
numbers}. Similarly, as the graph extends forever in the positive y direction but not in the negative y
direction, the range of f is {all positive real numbers} È {0}.
b. Just like the previous graph, we can draw the graph of f(x) = x
3
by plotting enough points as below.
Figure 2.18
-4 ...