Answer
a. False
b. True
c. False
d. True
Work Step by Step
$r(x) = \frac{(x^2+x)}{(x+1)(2x-4)}$
a. Vertical asymptote x=-1
False because even though x=-1 would render the function undefined, the numerator would equal to 0, thus there is no asymptote. Instead there will be a hole present in the function at x=-1
b. Vertical Asymptote x=2
True, this would cause the denominator to equal 0
c. Horizontal asymptote y = 1
False, the horizontal asymptote is the ratio of the leading term of the numerator over the leading term of the denominator. Thus the horizontal asymptote would be 1 (leading term of numerator) over 2 (leading term of numerator) = 1/2
d. Horizontal asymptote y=1/2
True, see the final sentence of part c.
