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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. Alert! A l e r t !

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3 Alert! Do­Now Begins! 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 observations. put x ­ 2 in parenthesis 1) 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? 1 2 ­2 ­2 0 ­1 0 2 2) Examine the graphs of the function and sketch them in your notebook ( two colors ). What do you notice about their relationship to one another?

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3 put x ­ 2 in parenthesis 1) 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? They are the opposite/ mirror image of one another. 1 2 The x and y values have ­2 ­2 switched places with each ­1 0 other. 0 2 2) Examine the graphs of the function and sketch them in your notebook ( two colors ). What do you notice about their relationship to one another? They are the opposite/mirror image of one another.The are reflected over the diagonal y = x

Announcements : A l e r t ! 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!)

Aim 4.3: How do we find the inverse of a function? HW: Worksheet 4.3 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, f ­1 (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 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? 0 ­ 2 3 4 Correct Correct HW: Worksheet 4.3 Correct Determining if the Inverse is a Function Determine whether or not the inverse of each relation graphed below is a function or not. A Horizontal line will hit the graph more than once Horizontal lines will only hit the graph once A Horizontal line will hit the graph more than once Horizontal lines will only hit the graph once

Aim 4.2: How do we perform operations with functions? HW: Worksheet 4.2, update notebooks What is an inverse function and how to we find it given a graph?

Classwork Time! Worksheet 4.3 • Complete Classwork independently Assess as You Work I got it! 1 • Check your answers with a partner. 2 I don't get it • If you get stuck, signal red . 3 I'm not sure