Inverses Inverse Relations & Inverse Functions What does it mean when two functions have an INVERSE relationship?

Activity Get a partner One person from the group get a piece of graph paper. The other person get a piece of notebook paper. Put BOTH of your names on both sheets.

Instructions Plot the following points on your graph. Connect the points. x y -1 4 6 2 7 5 8 10

Now plot these points on your graph in the same coordinate plane Now plot these points on your graph in the same coordinate plane. Connect the points. Then draw a dotted line for y=x. x y 4 -1 6 7 2 8 5 10

Questions What do you notice about the two graphs? What do you notice about the points? Do you think these points are inverse relationships? x y -1 4 6 2 7 5 8 10 x y 4 -1 6 7 2 8 5 10

Things you should notice: (facts about inverse relations/functions) Inverse relation – interchanges the input (x) values and output (y) values of the original relation Inverse relation graph – the result of reflecting the original graph over the line y=x

Finding inverse equations Question: All equations should be in what form? To find an inverse Flip the x and y. Solve for y. Your resulting equation will be in the form: y-1=

Examples y = 3x – 5 y = -x + 4

Note When taking the square root, you get two answers: a positive and negative. If given an f(x) function, do the same thing (flip x and y and solve). The answer will now be in f-1(x) form. It needs to be renamed.

Examples y = 4x2 f(x) = 8x – 2

Exit Ticket What is the inverse relation for the following points? {(0, 6), (-1, 2), (3, 4), (-5, -3)}