McGraw Hill Glencoe Algebra 2, 2012
MH
McGraw Hill Glencoe Algebra 2, 2012 View details
2. Inverse Functions and Relations
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Exercise 17 Page 396

First replace with Then, exchange the and variables. Finally, isolate

Inverse:
Graph:

Practice makes perfect

Let's begin by finding the inverse of the given function. Then we will graph the function and its inverse.

Finding the Inverse of the Function

Before we can find the inverse of the given function, we need to replace with
Now, to algebraically determine the inverse of the given equation, we exchange and and solve for
The result of isolating in the new equation will be the inverse of the given function.
Solve for
Finally, we write the inverse of the given equation in function notation by replacing with in our new equation.

Graphing the Function

Because the given function is a straight line, to draw the graph we should first determine its slope and intercept.
The slope is . The intercept is so the graph crosses the axis at the point A slope of means that for every unit we move in the positive horizontal direction, we move units in the negative vertical direction.
To graph the equation, plot the intercept and then use the slope to find another point on the line.

Graphing the Inverse of the Function

Finally, we can graph the inverse of the function by reflecting the straight line across the line This means that we should interchange the and coordinates of the points that are on the straight line.

Points Reflection across

Let's plot and connect the obtained points.