How do I perform transformations of functions?

[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?

thanks in advance.

 

[hotvette]

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

 

[Intr3pid]

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

thanks in advance

 

[UnD]

The easiest way is plot points.

 

[Intr3pid]

can anyone give a solution? not just unfinished sentences.

 

[quantumdude]

The easiest way is plot points.

No, in fact that's the hardest way!

say f(x) = x^2-5 , how do I graph 1/f(x)

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?

 

[Intr3pid]

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

 

[ivybond]

hi everyone
I have trouble ... not knowing how draw graphs of recipricol transformations (of functions).

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.

 

[hotvette]

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

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?)

 

[professor]

what I've 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