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Chapter 2: Problem 73

Describe how to use the graph of a one-to-one function to draw the graph of its inverse function.

Short Answer

Expert verified
To sketch the graph of the inverse of a function, reflect the graph of the original function over the line y = x. Each point (a, b) on the graph of the original function corresponds to a point (b, a) on the graph of its inverse.

Step by step solution

01

Recognize One-to-One Function

A function is one-to-one if every x value correspond to exactly one unique y value. Identify the one-to-one function given and ensure that it fits this criterion.
02

Draw the Function's Graph

Plot the given function's graph. Use a suitable scale to make sure all important points are visible.
03

Observe Line of Reflection

The key in graphing the inverse of a function is to understand that this transformation reflects the graph of the original function over the line y = x. Draw this line on the same coordinate plane.
04

Reflect Original Points

Each point on the graph of a function corresponds to a point on the graph of its inverse. If the original function contains the point (a, b), then its inverse contains the point (b, a). Reflect every point on the function's graph over the line y = x.
05

Draw the Inverse Function

Connect the reflected points with a smooth curve to draw the graph of the inverse function. Make sure this graph is a reflection of the original function over the line y = x.

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Most popular questions from this chapter

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