# 005 Sample Final A, Question 20

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Question Consider the following rational function,

${\displaystyle f(x)={\frac {x^{2}+x-2}{x^{2}-1}}}$

a. What is the domain of f?
b. What are the x and y-intercepts of f?
c. What are the vertical and horizontal asymptotes of f, if any? Does f have any holes?
d. Graph f(x). Make sure to include the information you found above.

Final Answers
a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, ${\displaystyle a_{n}=(-a)^{n}}$
b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
c) False. ${\displaystyle y=x^{2}}$ does not have an inverse.
d) True. ${\displaystyle cos^{2}(x)-cos(x)=0}$ has multiple solutions.
e) True.
f) False.