aChoose the correct graph below b What is the domain of the

a.)Choose the correct graph below

(b) What is the domain of the given? function? Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice. What is the range of the given? function? Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.

(c) What? is/are the vertical? asymptote(s)? Select the correct choice below? and, if? necessary, fill in the answer? box(es) to complete your choice.

(d)What? is/are the horizontal? asymptote(s)? Select the correct choice below? and, if? necessary, fill in the answer? box(es) to complete your choice

Solution

f(x)= -3 + 2/(x-4)^2= -3(x^2+16-8x+2)/(x^2 + 16-8x)

                           = -3x^2 +24x-50/x^2 +16-8x

Here the degree of the to and bottom is same

therefore horizontal asymptote ,y= leading coefficient of top/leading coefficient of bottom=-3

the given function is a rational function and the rational function is undefined when the bottom is zero

therefore (x-4)^2=0

that gives x=4

therefore the domain is

(-inf,4)U(4,inf)

therefore y=-3 is the horizontal asymptote

and for vertical asymptote,we have to set the bottom to zero

that is(x-4)^0= x=4

therefore the correct graph is D