Question

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

Answer 1

Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1

Step-by-step explanation:

$f(x) = \dfrac{1}{x-2}+1$

Vertical Asymptote is the restriction on the x-value.  The denominator cannot be zero, so x - 2 ≠ 0  ⇒  x ≠ 2

The restricted value on x is when x = 2  which is the vertical asymptote

Horizontal Asymptote (H.A.) is the restriction on the y-value.  This is a comparison of the numerator (n) and denominator (m).  There are 3 rules that will help you:

• n > m    No H.A. (use long division to find slant asymptote)
• n = m    H.A. is the coefficient of n divided by coefficient of m
• n < m    H.A. is 0

In the given problem, n < m so y = 0, however there is also a vertical shift of up 1 so the H.A. also shifts up.  This results in H.A. of y = 1