Question

What is the oblique asymptote of the function f(x)= x^2+4x+5/x+3
a) y=x+3
b) y=x+1
c) y=x-1
d) y=x-3

Answer 1

Ok, so first what is one incorrect answer?

Answer 2

Do you still need help with this?

Answer 3

to find oblique asymptotes, you have to divide the numerator by the denominator, either using polynomial long division or synthetic division

since you're dividing by x + 3, we assume x + 3 = 0 and therefore our divisor is -3

x^2+4x+5 is the dividend, and the coefficients are 1, 4, and 5

so the synthetic division is set up as:



here are the steps for synthetic division: https://www.purplemath.com/modules/synthdiv.htm

(if you are having trouble understanding the link, I would also be willing to walk you through the steps)