Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1
<u>Step-by-step explanation:</u>
<u>Vertical Asymptote</u> 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 <em>which is the vertical asymptote</em>
<u>Horizontal Asymptote</u> (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
