SOLUTION: Give an example of a rational function that fulfills
the description.
a. A rational function that has a vertical asymptote
at -5 and a hole at 7.
b. A rational function that
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-> SOLUTION: Give an example of a rational function that fulfills
the description.
a. A rational function that has a vertical asymptote
at -5 and a hole at 7.
b. A rational function that
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Question 1104537: Give an example of a rational function that fulfills
the description.
a. A rational function that has a vertical asymptote
at -5 and a hole at 7.
b. A rational function that has no vertical asymptote
and does have a slant asymptote Found 2 solutions by greenestamps, Edwin McCravy:Answer by greenestamps(13209) (Show Source):
a. A rational function that has a vertical asymptote at -5 and a hole at 7.
The graph of a rational function has a hole at x=a if there are linear factors of (x-a) in both numerator and denominator.
The graph of a rational function has a vertical asymptote at x=a if there is a linear factor of x-a in the denominator but not in the numerator.
So to get a vertical asymptote at x=-5 there must be a factor of (x+5) in the denominator but not in the numerator; to get a hole at x=7 there must be a factor of (x-7) in both numerator and denominator .
The simplest rational function with those factors is
b. A rational function that has no vertical asymptote and does have a slant asymptote
The graph of a rational function has a slant asymptote if the degree of the numerator is 1 greater than the degree of the denominator.
Assuming for simplicity that there are no holes in the graph, caused by identical linear factors in both numerator and denominator, then if the graph of a rational function has NO vertical asymptotes, then there are no linear factors in the denominator. That means the denominator has no real zeros.
So a rational function that has a slant asymptote but no vertical asymptote must have a denominator with no real zeros, and a numerator with degree 1 greater than the degree of the denominator.
You can put this solution on YOUR website! Give an example of a rational function that fulfills
the description.
a. A rational function that has a vertical asymptote
at -5 and a hole at 7.
It needs to have factor (x+5) in the denominator only to have an asymptote
at x=-5.
It needs to have a factor (x-7) in both the numerator and denominator to
have a hole at x=7.
So I'll make up another factor for the numerator, say (4x+21)
b. A rational function that has no vertical asymptote
and does have a slant asymptote
I'll work on it
Edwin
