Topic #2: Understanding Inverse RelationsAfter completing the topic Understanding inverse

relations, students willunderstand the graphical, tabular, and algebraic

relationship between a linear function and its inverse;

understand the relationship between exponential and logarithmic functions;

understand the relationship between quadratic and square root functions;

identify one-to-one functions; be able to restrict the domain of a quadratic

function in order for its inverse to be a function.

Finding an InverseSteps for finding the inverse of a function

1. Change f(x) y2. Exchange x and y in the equation3. Solve the equation for y4. Replace y with

Example: f(x) = 2x – 5 )(1 xf

Drill1. Find the inverse of the function,

2. Then graph the function and its inverse on the same graph. (Label both functions).

Graph the line y = x on the same graph to show that the two functions are inverses.

23

2)( xxf

Drill1. Find the inverse of the function,

2. Then graph the function and its inverse on the same graph. (Label both functions).

Graph the line y = x on the same graph to show that the two functions are inverses.

Homework: Staple together homework #7, 8, and 9. Due after the drill

23

1)( xxf

Drill1. Graph the function,(Make a table of values)

2. Identify the domain and range of the function (using the graph)

3. Graph the inverse of the function on the same graph (invert the original table of value)

4. Using the domain and range from #2 to help you, identify the domain and range of the inverse.

5. Identify the equation of inverse.

xxf 2)(

DrillFind the inverse of the following functions:

1.

2.

3.

54

3)( xxf

xxf 6)(

2)5()( 2 xxf

DrillWhich of the following functions is Quadratic?

X Y

-2 4

-1 7

0 12

1 19

X Y

0 -2

1 0

2 3

3 8

Topic #2 ReviewGet out a clean sheet of notebook paper and

label it:

Topic #2 Review: Understanding Inverse Relations

Copy all problems, show all work.