Write a radical function

Question

Write a rational function f that has the specified characteristic, (There are MANY correct answers to this question) Vertical Asymptote : x = 2 Horizontal Asymptote y = 1/2 Zero: x = 1

Answer 1

y = (x-1)/[2(x-2)]

vertical asymptote at x=2: (x-2) appears in denominator

zero solution at x=1: (x-1) appears in numerator

Horizontal asymptote at y = 1/2 ---> limit must be 1/2 as x-->infinity

k * lim x-1

----- = 1/2

x-2

k * 1 = 1/2 <-- L'hopital's;s rule or divide everything by x

k=1/2

you can do (1 - 1/x) over (1 - 2/x)

then as x-->infinity, the limit is 1,

so k=1/2

the rational function is y = (x-1)/[2(x-2)] = (x-1)/(2x-4)