Algebra Know-It-ALL

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.