1. ## functions and relations

Hey
Can someone explain to me how to start each of the attatched (in the links) questions?
I know how to do the actual math, Im just having troubles starting them

Thanks so much!
10:10 on Flickr - Photo Sharing!
7 8 9:
7 8 9 on Flickr - Photo Sharing!
6: 6 on Flickr - Photo Sharing!
5: 5 on Flickr - Photo Sharing!
3 4: 3,4 on Flickr - Photo Sharing!

2. Your question go from trig to inverse to sketching to combining functions to completing the square, topics which tend to be distinct from each other in high school. If you cannot do them I would suggest going back to the basics...

7) root functions and quadratics -- the key is to use transformations and algebraic manipulation (factor, complete the square) to find key features such as maximums and minimums and points at which the graph crosses the x-axis. 7(d) is a rational function, find a common base.

8) Inverse functions have the property of x = y, the opposite of the normal y=x. If it's a rational function areas where the denominator = 0 are undefined so include them as restrictions.

9) Sketch it using the techniques in 7). (a) break even are points where the function = 0. (b) Profit maximization occurs where the function is at it's max, so complete the square to get the vertex.

3. Thanks

I understand all of that except for 7d)
what do you mean by "find a common base"?

4. You need to change the function to make it easier to find the features...

$\frac{3}{x-1} - 2$

$=\frac{3-(2)(x-1)}{x-1}$

$=\frac{3-2x+2}{x-1}$

$=\frac{-2x+5}{x-1}$