Homework:

Warm-up:Review 9.c adding and subtracting rational expressions

GET OUT YOUR 9.c NOTES!!!

Same denominator?

add (or subtract) numeratorskeep same denominator

Example 1:

 Different denominators? You must build a LCD!!!1. Factor each denominator completely.2. Multiply each fraction, top and bottom,

by any factors from the other fraction that it is missing.

3. Write as one fraction BEFORE you do any multiplying out.

4. Multiply out numerator and collect like terms.

5. Factor numerator and reduce if possible.

Example 2:

Example 3:

Example 4:

You do some!

Answers:

8.d Find and Graph the Inverse of a Function or Relation [8.8]

After this lesson you will be able to…

Find and graph the inverse of a function.

Determine whether 2 functions are inverses of each other.

What do you think of when you hear “inverse”?

Inverse FunctionsAn inverse function will take ananswer from the original function and “undo” it to give you back the x-value that produced the answer.

If original function is called ________ then the inverse is called _________.

Example 1:

1. Let’s pick an x-value and get an answer so we can test the inverse!

2. Put the answer into the inverse.3. You should get the original x-value

back!

1 4( ) 5 4 and ( )

5x

f x x f x

Let’s test another!

12 2 12( ) 6 and ( )

3 3x

f x x f x

Building your own inverse!1. Replace f(x) with y (it is just

easier to look at that way).2. Switch the x and y in the

equation.3. Resolve the equation for y.4. The result is the inverse.5. Now check by using an x-value

in the original!

Example 3:

1. Build the inverse.2. Choose an x-value to use in

the original, plug answer into inverse. Did it work?

3. Graph the original and it’s inverse on the same graph.

( ) 6 5g x x

Example 4:

1. Build the inverse.2. Choose an x-value to use in

the original, plug answer into inverse. Did it work?

3. Graph the original and it’s inverse on the same graph.

3( ) 1

5p x x

WOW!

Inverse functions _______________________ over ____________________!!!

Homework:

HW ST 8.d