Algebra Know-It-ALL

230 The Cartesian Plane

When we want to graph the inverse of a relation, we “flip the whole graph over” along a “hinge” cor-

responding to the “point reflector.” That moves every point in the graph of the original relation to its new

position in the graph of the inverse. When we do this to the graphs from Figs. 14-4, 14-5, and 14-6, we

get the graphs in Figs.14-8, 14-9, and 14-10 respectively. These graphs show the inverses of the original

three relations. Note that the positions of the x and y axes have not been switched, but the values of the

variables, as well as the domain and range, have been!

–6 –4 –2 246

2

4

6

–2

–4

–6

x

y

"Point

reflector"

line

Original y=x

Inverse

Original

Inverse

Original

Inverse

Original

Inverse

Figure 14-7 Any point in the graph of the inverse of a

relation can be located on the basis of its

“mate” in the graph of the original relation.

–6 –2 246

2

4

6

–2

–4

x

y

(5,3)

(0,–2)

(–4,–6)

Figure 14-8 Cartesian graph of the relation y=x− 2.