Bell work: Problemabhkasymptote (y=k) point #1 (h, a+k) point #2 (h+1,ab+k) y=-2 x+3 +1 Fill in the table for the indicated problem and sketch a graph:

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Presentation transcript:

Bell work: Problemabhkasymptote (y=k) point #1 (h, a+k) point #2 (h+1,ab+k) y=-2 x+3 +1 Fill in the table for the indicated problem and sketch a graph:

Inverse Functions Inverses are used to solve equations. Any time we “undo” operations to solve for x, we are using the corresponding inverse functions… is inverse to Square is inverse to square root. and more…

End in Mind The equation used to convert from degrees Celsius to Fahrenheit is Write an equation we can use to convert from degrees Fahrenheit to Celsius.

Function: A relation in which each input has exactly one output. Recall… Functions have different representations. Table Equation Graph xy ***Remember, not all the ordered pairs appear in the table. There are too many!*** y=f(x)

Inverse: The relation formed by switching the inputs and outputs of the function. Just switch x and y!!! xy xy Function:Inverse: TABLE:

Inverse: The relation formed by switching the inputs and outputs of the function. Just switch x and y!!! Function:Inverse: GRAPH:

Graphing the inverse: The graph of the inverse is flipped over the line Function: Inverse:

You try graphing the inverse. In class handout.

How can we tell if the inverse will be a function? One-to-One Function: A function in which each output has exactly one input. One-to-oneNot one-to-one Horizontal Line Test: If ANY horizontal line cuts the graph more than once, then the function is NOT one-to-one.

How can we tell if the inverse will be a function? FACT: If a function is one-to-one, then the inverse is a function. Function Not a function ***Confirm this with the vertical line test for functions.***

Notation: When a function, f is one-to-one, we can write the inverse in function notation to represent the output when the input x is plugged into EX: If Meaning, we plug in -2 and get 5. then

How to write the equation for the inverse function. EX1: Find the inverse of STEP 1:Replace f(x) with y. STEP 2:Switch x and y. STEP 3:Solve for y. STEP 4:Replace y with

How to write the equation for the inverse function. EX2: Find the inverse of STEP 1:Replace f(x) with y. STEP 2:Switch x and y. STEP 3:Solve for y. STEP 4:Replace y with Cube root both sides!!!

How to write the equation for the inverse function. EX3: Find the inverse of NO INVERSE! This function is NOT one-to-one and therefore, no inverse exists.

Practice finding inverse functions of one-to-one functions. Be sure to make sure each function is actually one-to-one. If it is not, there is not inverse. Think about what type of functions will be one-to-one versus which ones will not (You could even jot some notes in your parent function booklet!)