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

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation:

lol 2

step-by-step explanation: