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AIM (4.3) : How do we find the inverse of a function?

Take two minutes to get your Notebooks, Signals, Calculators, & Student Orgzniers before we begin today's lesson.

A l e r t !

Do­Now Begins!

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3

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Examine the table of values for each function and complete the blanks below. What do you notice about the tables in relation to each other? Examine the graphs of the function and sketch them in your notebook (two colors). What do you notice about their relationship to one another?

1

­1 ­2

Today we will look at different inverse functions in depth. Using your graphing calculator, put each function into the graphing calculator at the same time and state your

• bservations.

1) 2)

put x ­ 2 in parenthesis

2

­2 2

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3 Examine the table of values for each function and complete the blanks below. What do you notice about the tables in relation to each other? Examine the graphs of the function and sketch them in your notebook (two colors). What do you notice about their relationship to one another?

1

­1 ­2

1) 2)

put x ­ 2 in parenthesis

2

­2 2

They are the opposite/mirror image of one another.The are reflected over the diagonal y = x They are the opposite/ mirror image of one another. The x and y values have switched places with each

• ther.

Announcements: 1) Notebook Check ­ Next Tuesday 2) Tutoring: Mr. Lo is available after school Monday & Friday: Right after school 3) MACS Robotics club meets every Wednesday, room 207B (extra credit!)

A l e r t !

Inverse Function

A function that will "undo" anything that the original function does

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3

Graphs of Inverse Functions

The "Do Now" demonstrated that to graph an inverse function, you can simply switch the x and y values of the original function and plot them. Hence, the inverse function, f­1(x), is a reflection of the original function over the line y = x.

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3

Determining if the Inverse is a Function

How do we test a graph to determine if it is a function? What would be the opposite of this test?

To quickly determine if a function's inverse is a function, do a horizontal line test Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3

Determining if the Inverse is a Function

Determine whether or not the inverse of each graph below is a function or not.

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3

Determining if the Inverse is a Function

Determine whether or not the inverse of each relation graphed below is a function or not.

4 Correct 0 ­ 2 Correct 3 Correct

Horizontal lines will only hit the graph once Horizontal lines will only hit the graph once

A Horizontal line will hit the graph more than once A Horizontal line will hit the graph more than once

What is an inverse function and how to we find it given a graph?

Aim 4.2: How do we perform operations with functions? HW: Worksheet 4.2, update notebooks

Classwork Time! Worksheet 4.3

Assess as You Work

1 3

I got it! I don't get it I'm not sure

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• Complete Classwork independently
• Check your answers with a partner.
• If you get stuck, signal red.