Question

r(x)=x^2-49/x^4-16 Any help would be appreciated...

1) factor the numertor and denominator of R and Find it's domain-
2) Find Real Zero's- of numberator
3) Find Real Zero's of denominator
4) locate any horizontal or obliqe asymptote(Which I have a horizontal of y=0)
5) using the real zeors of the numertor and denominator- divide the x-axis
6) Analyze the behavior of the graph
7) Put together and graph
Any help to get me started would be appreciated, I am just stuck at how to even start the problem.

Answer 1

Both numerator and the denominator is of the "special products" category. They are the difference of two perfect squares and equate to:

(x+7)(x-7)
--------------
x^2 + 4)(x^2-4)

The denominator still can be factored further as it still has the difference of two perfect squares.

Answer 2

factoring further the fraction:

(x+7)(x-7)
r(x) =---------------------
(x^2+4)(x+2)(x-2)
You can now calculate it domain.

Answer 3

Any value of x that results in denominator value of 0 would be excluded as a division by zero (0) is not permitted.

Answer 4

I got (-∞,-2)U(2,2)(2,∞)

Answer 5

Both +2 and -2 would be excluded from the domain.

Answer 6

2.) + or - 7

Answer 7

3.) + or - 2

Answer 8

On number 4.0 I don't know where y comes in to play, I think that is a typo and they mean "r"

Answer 9

There is a r for x=0, it is 3.0625

Answer 10

I suggest you let Wolfram graph the function for you. http://www.wolframalpha.com/input/?i=%28x%5E2-49%29%2F%28x%5E4-16%29

Answer 11

so would I use the r(x)=x^2-49/x^4-16 to do the graph OR (x+7)(x-7) one. And on #4 can you show me how you got that answer? Im confused..

Answer 12

I am losing my internet connection, severe storm and I use satellite which fails in heavy rain.