How do you write a rational function that has the

klamytewoc

klamytewoc

Answered question

2022-02-18

How do you write a rational function that has the following properties: a zero at x= 4, a hole at x= 7, a vertical asymptote at x= -3, a horizontal asymptote at y=25?

Answer & Explanation

emeriinb4r

emeriinb4r

Beginner2022-02-19Added 10 answers

A zero at x=4 means we have (x-4) as a factor in numerator;
a hole at x=7 means, we have x-7 a factor both in numerator as well as denominator;
a vertical asymptote at x=-3 means x+3 a factor in denominator only
a horizontal asymptote at y=25 means highesr degrees in both numerator and denominator are equal and their coefficients are in ratio of 2:5
Hence desired rational function is 2(x4)(x7)5(x7)(x+3)
i.e. 2x222x+565x220x105
See its graph down below. Observe vertical asymptote x=-3 and horizontal asymptote y=25. We have a zero at x=4 as functtion passes through (4,0). Hole is not seen as x-7 cancels out, but we know, the function is not definedat this point.
graph{2x222x+565x220x105[10.67,9.33,4.4,5.6]}1

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