Tuesday, March 8, 2011

Tuesday, March 8th, 2011 Lesson 8.2

Today in class we went over the homework we had over the weekend which was 801, then viewed the blog. Mr. Cope gave us the rubric on how we would be graded for the blog posts, then started the lesson.
Lesson 8.2: Inverses of Relations
3 Important things to know about inverses of relations:

Suppose f is a relation and g is the inverse of f;

1) A rule (or equation) can be found by switching x and y (solving for y if necessary)

2) A graph for g is found by reflecting f over y=x,

3) The domain of g is the range of f, and the range of g is the domain of f

An example of inverse relation is this;
Let f = (1,4) (2,8) (3,8) (0,0) (-1,-4)

The inverse relation of this would be;
(4,1) (8,2) (8,3) (0,0) (-4,-1)

Another thing to note, is that the f is a function but the inverse of f is not.
This is because when you reverse x and y, there becomes (8,2) and (8,3) which means it is not a function.
You can also find out if the inverse is a function by seeing if it passes the horizontal line test.

The domain of f is ( 1, 2, 3, 0, -1) and the range is ( 4, 8, 0, -4)

The domain of the inverse is (4, 8, 0, -4) and the range is (1, 2, 3, 0, -1)
You should note that the domain and range swap when it is the inverse.

Another example is f 9x0 = 1/2x + 4
The work I did to find the inverse is;
I rewrote the equation to be y = 1/2x + 4
Then rewrote it as x = 1/2y + 4
Then I subtracted the 4
So its now x - 4 = 1/2y
Then I multiplied both sides by 2 to get ride of the fraction
So it would now be 2x-8 = y which is the final answer.

I hope this helps!

Homework :
802 and the 3 problems on the back of the worksheet.

The next scribe will be Leah.

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