# Homework Help: Transformations of functions

1. Oct 14, 2005

### Intr3pid

hi everyone

I have trouble recognizing expansions/compressions, and not knowing how draw graphs of recipricol transformations (of functions). can someone explain to me how to "do" them? or recommend a site that has a tutorial about it?

2. Oct 14, 2005

### hotvette

It might help to provide a specific example and explain where/how you are having trouble

3. Oct 14, 2005

### Intr3pid

say f(x) = x^2-5 , how do I graph 1/f(x). Please give an in depth explanation.

4. Oct 14, 2005

### UnD

The easiest way is plot points.

5. Oct 17, 2005

### Intr3pid

can anyone give a solution? not just unfinished sentences.

6. Oct 17, 2005

### Tom Mattson

Staff Emeritus
No, in fact that's the hardest way!

When graphing rational functions in general, it is best to start by finding the following:

1.) x-intercepts
2.) y-intercepts
3.) Vertical asymptotes
4.) Horizontal asymptotes
5.) Slant asymptotes

Which of these do you know how to find?

7. Oct 22, 2005

### Intr3pid

i really need help, i don't get what you guys are saying.

8. Oct 23, 2005

### ivybond

What textbook are you using?
Does it have paragraphs "Rational Functions and Asymptotes" and
"Graphs of Rational Functions"?
g(x) = 1/f(x) is a rational function.

9. Oct 25, 2005

### hotvette

Tom Mattson had it right. You need to look for intercepts and asymptotes. Look at the reciprocal function:

$$g(x)=\frac{1}{x^2-5}$$

You need to consider what values of x will cause the function to go to zero, infinity, etc. It's always good to look at limits as x goes to zero and to infinity. You also need to consider what value of x will make the denominator go to zero (meaning what for the value of the function?)

10. Oct 25, 2005

### professor

what ive atleast been told, ad seems to be a fairly easy way to look at it is to call all the x values in the equation y, then all the y values x ( f(x) for ex would be y.. the changed to x ) first of all, then to solve for y -

: the first part i allways found confuzing, and useless at best, so in otherwords just switch around the equation to solve for X after you have named f(x) or f(q) or whatever "Y".

and oh yes- as mentioned above, make sure to disclude answers that will give you nonreal numbers