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Evaluation of a Function

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A certain rational function f(x) contains quadratic functions in both its numerator and denominator. Aside from that, we also know the folliwing things about f:
f has a vertical asymptote at x=5
f has a single x-intercept of x=2
f is removably discontinous at x=1, lim as (x)approaches 1 of f(x)= -1/9
evaluate lim of f(x)as x approaches infinity

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A function is evaluated given a group of parameters. The solution is detailed and well presented.

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Problem:
A certain rational function f(x) contains quadratic functions in both its numerator and denominator. Aside from that, we also know the following things about f:
• f has a vertical asymptote at x = 5
• f has a single x-intercept of x = 2
• f is removably discontinuous at x = 1, since
• Evaluate

Solution:
If f has a vertical asymptote at x = 5, then the factor (x-5) must appear in the denominator but not the numerator. Why is this? When we plug x = 5 into our function f, we want to get a 0 in the denominator but not the numerator; mathematically, this means an asymptote must appear ...

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