can you help me please? r (x) =x^2 + x - 6/ x^2 - 25

A

alparnell

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I was given the problem above:

X^2 + x - 6/ x^2 - 25.

1. List the x intercepts in ordered pair form.
2. List the y intercept in ordered pair form.
3. List the vertical asymptotes.
4. List the horizontal asymptotes. Explain answer.
5. Draw the graph including all steps above.

I missed a week of class due to a death in the family and am now lost on how to do all of this. If someone could help me and explain the steps so I can learn how I would be grateful as I can't meet with the instructor until after the test on this. Thank you so much.
(I have several more just like this!)
 
alparnell said:
I was given the problem above:

X^2 + x - 6/ x^2 - 25.

1. List the x intercepts in ordered pair form.
2. List the y intercept in ordered pair form.
3. List the vertical asymptotes.
4. List the horizontal asymptotes. Explain answer.
5. Draw the graph including all steps above.

I missed a week of class due to a death in the family and am now lost on how to do all of this. If someone could help me and explain the steps so I can learn how I would be grateful as I can't meet with the instructor until after the test on this. Thank you so much.
(I have several more just like this!)
Click to expand...
First, please state the problem clearly. Is it x^2+ x- (6/x^2)- 25, which is what you wrote but probably NOT what you mean, or is it (x^2+ x- 6)/(x^2- 25)?

1) Do you know what an x-intercept is? It is a point at the graph on which y= 0. What would x be then?
2) Do you know what a y-intercept is? It is a point on the graph at which x= 0. What would y be then?
3) A vertical asymptote is a value such that y goes to infinity or negative infinity as x approaches that value. You may remember that a fraction goes to infinity as the denominator goes to 0. Where is the denominator equal to 0 and the numerator not? It might help to factor the numerator and denominator.
4) There is a horizontal asymptote if the function approaches some fixed number as x goes to infinity. Since the leading coefficient of both numerator and denominator is x^2, this is equal to 1+ some fraction.
5) Put all of the information from (1) to (4) together with a few calculated points.
 
I'm sorry. I meant the second option. I thank you for your help. If I were to state my answers could you tell me if I'm right? Truly thankful....
 
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