Question

identify the vertical and horizontal asymptote for f(x)=(x^2+3)/(x-4).

Answer 1

as x tends to 4, the value of f(x) tends to infinity from both sides, you can say x=4 is one horizontal asymptote

Answer 2

A plot is attached.

Answer 3

finding the vertical asymptotes are easy... just set each factor in the denominator = 0 and solve. the x-values that makes the denominator 0 will (MOST of the time) be your vertical aymptote.

Answer 4

for horizontal asymptotes to occur, the degree on the numerator has to be equal (or less) than the degree of the denominator.
if the degree of the numerator is less than the degree of the denominator, then the line y=0 is your horizontal asymptote.

Answer 5

if the degree of the numerator is equal to the degree of the denominator, then y=a/b is your asymptote, where a, b are the coefficients of the terms with the highest degree.

Answer 6

for this function, f(x)=(x^2+3)/(x-4), the degree on the top is greater than the degree on the bottom. There is no horizontal asymptote here.

Answer 7

but there is a slant asymptote...