Tuesday, March 8, 2011

3/8/11 8-2 Inverses of Relations

At the start of class we went over homework for aprox 30 minutes. After going through the homework in the class we got 8-2 work sheet for the new section that the class is learning.

Earlier in the year from chapter one the class learned about Functions, Range, domain, and inverse. In this section the class built on top of the previouse chapters where we learned about Functions.
A Function is a relationship that has exactly one output for each input.
ex 1. f={(4,1) (5,9) (6,9)} This is a function because for each input there is one ouput and there are no repeating inputs.
ex 2. f={(4,5) (4,4) (6,9)} This is not a function because there are repeating inputs for the outputs.

The domain of a function is all possible input values for X which allows the function to work.

ex. The domain for ex 1. is {4,5,6}
ex. The domain for ex 2. is {4,4,6}

The range is the set of all possible output values usally Y.
ex. The range for ex 1. is {1,9}
ex. The range for ex. 2 is {5,4,9}

Inverse is the opposite of an equation.
ex 1. f={(8,9) (7,8) (4,3)} Inverse of the function is f={(9,8) (8,7) (3,4)}

Today we learned three important rules.
A) A rule for y can be found by switching x & y and solving for Y

B) A graph for y is found by reflecting F over the line y = x.

C) Domain of G is the range of E The range of G is the Domain E

Inverse of a function.
If the inverse of a function does not have a repeating x input then it is a function but if the x input repeats the inverse is not a function.
example of a inverse being a function. - { 1,1 2,2 3,3} inverse of function { 1,1 2,2 3,3}
example of a inverse not being a function. - {1.3 2,3 4,5} ineverse of the function { 3,1 3,2 5,4} the inverse is not a function because the x inputs repeat.

Inveres in equations.
if f(x)= 1/2 x + 4 the steps to finding the inverse would be
step 1 put the y in place of x so that the equation equals x = 1/2 y + 4
step 2 then subtract four from both sides -4 + x = 1/2 y + 4 + -4
step 3 mutiply by 2 on both sides 2(x + -4) = (1/2 y)2
step 4 the inverse of the equation is 2x + -8 = y

Inverse of a graph
Early in the year we learned the line test to check if the graph was a function.
View earlier notes

If the line does not touch twice on the same point then it is a function
if it touches twice on a line then it is not a function.
To get the inverse of a graph just simply replot the point on the opposite axis such as if 3,1 is the point the plot 1,3 for the inverse.

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