For what values of  a  and  m  does  f(x) have a horizontal asymptote at  y  =  2 and a vertical asymptote at  x  =  1?

ANSWER

a=-1,m=1

EXPLANATION

The given function is

For this rational function to have a horizontal asymptote at y=2, the degree of the numerator must equal the degree of the denominator.

This implies that, we must have m=1.

For the function to have a vertical asymptote at x=1, then,

This implies that,

The correct choice is the third option.

for a rational expression the vertical asymptotes occur when the denominator equals 0, in this case that will be when x + a = 0.

now, if there were to be a vertical asymptote of x = 1, that simply means that

x = 1 ==> x - 1 = 0.

meaning that a = -1.

horizontal asymptotes occur when the denominator has a higher degree than the numerator OR when both have the same degree.

when the degree of the denominator is higher, then the only horizontal asymptote occurring is y = 0.

when the degrees are the same, then the horizontal asymptote occurs at the leading terms' coefficient fraction.

now, if this expression were to have a horizontal asymptote of y = 2, that simply means

v,jhvljh,b.b; hk; ljujb,vuvccklokll; k,m,km,

step-by-step explanation: