232 The Cartesian Plane
Three Functions
The process for graphing a function is the same as it is for graphing a relation. Remember, a
function is nothing more than a relation with special properties! In this section, we’ll look at
the graphs of the three functions we evaluated in Chap. 13.
Add 1 to the input
Figure 14-11 shows some points plotted in Cartesian coordinates, along with the straight line
that connects them, for the following function:
y=x+ 1
These points lie along a straight line. Note the similarity between this graph and the one shown in
Fig. 14-4. The only difference here is that the line is exactly 1 unit lower on the coordinate plane.
Square the input
In Fig. 14-12, several points are plotted, and the curve connecting them is drawn, for the function
w=v^2
This graph is the same curve as the one shown in Fig. 14-9, but the variable names are different.
Cube the input
Figure 14-13 shows what happens when the independent variable is cubed rather than squared.
Several points, along with the curve connecting them, are plotted for the function
u=t^3
–6 246
2
4
6
–2
–4
–6
x
y
(0,1)
(–4,–3)
(4,5)
Figure 14-11 Cartesian graph of the function y=x+ 1.