Q. 99 - Precalculus Enhanced with Graphing Utilities

Question

Draw the graph of a one-to-one function that contains the points  $\left(-2,-3\right),\left(0,0\right), and \left(1,5\right).$ Now draw the graph of its inverse. Compare your graph to those of other students. Discuss any similarities. What differences do you see?

Step-by-Step Solution

Answer

The graph of one-to-one and its inverse is

Step 1. Given Information

The given points are $\left(-2,-3\right),\left(0,0\right), and \left(1,5\right).$

We have to draw the graph of a one-to-one function that contains the points and draw the graph of its inverse.

Step 2. Sketch the graph

The graph of a one-to-one function that contains the points and its inverse is

As the points $\left(a,b\right)$ are of a one-to-one function on the graph then $(b,a)$ points will lie on its inverse function of the graph.

The dotted line in the graph represented the inverse function graph.

The graph of the one-to-one function and its inverse will be symmetrical to the line $y=x.$