2.5 Inverses Warm-up (IN) Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function.

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Presentation transcript:

2.5 Inverses Warm-up (IN) Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function. Solve each equation for y.

Notes Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function. Inverse of a function - Domain and range are switched Ex 1 – find the inverse of each relation and determine if it’s a function. Not a function Yes a function

Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function. Ex 2 – Find an equation for the inverse of the equation Switch the x and y, then solve for y!

Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function. Try it! How can we use inverses in the real world??

How are the graphs of a function and its inverse related? Graph y=x and y=3x-2 and its inverse (use the inverse key) on the same viewing screen. Repeat with y=3x+2, y=-2x+5 and y=x² **W2L! Explain how the graphs of a function and its inverse are related. Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function.

Horizontal Line Test – Used to determine if the inverse of a function is a function Ex 3 – Is the inverse of the graph a function? a. b. c. yes no yes

Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function. One to One Function – Passes the horizontal line test, its inverse is also a function. 2 functions are inverses of each other if and

Ex 4 – Try it! Pg. 122 #10

HW – p. 122 #11,19,21,27,28,30-48(mult. of 3), 51, 52 Out – Describe (in words!) the procedure for finding the inverse of y=4x-1. Summary – I think I can remember… POW!!