SOLUTION: SOLUTION: I am a rational function having a vertical asymptote at the lines x = 3 and x = -3, and a horizontal asymptote y = 1. If my only x-intercept is 5, and y-intercept is -5/9

SOLUTION: SOLUTION: I am a rational function having a vertical asymptote at the lines x = 3 and x = -3, and a horizontal asymptote y = 1. If my only x-intercept is 5, and y-intercept is -5/9

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Question 1143053: SOLUTION: I am a rational function having a vertical asymptote at the lines x = 3 and x = -3, and a horizontal asymptote y = 1. If my only x-intercept is 5, and y-intercept is -5/9, What Function am I ?
Please help me to solve this problem by step by step , showing solution and graph, and final answer thanks po
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I don't think this is possible.

If the function has vertical asymptotes of 3 and -3, then the denominator of the function must have factors of

and

, hence the denominator must be

.

If the function has a non-zero constant as a horizontal asymptote, then the degree of the numerator function must be the same as the degree of the denominator function. Consequently, the degree of the numerator function in this case must be 2.

And if the only

-intercept is 5, then the numerator function has to be

or

.

However, if our function is

, then the

-intercept must be

, not

as specified.

On the other hand, if the function is

so that the vertical asymptotes, the

-intercept, and the

-intercept are as specified, then the horizontal asymptote would be

rather than

as required.

John

My calculator said it, I believe it, that settles it

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