005 Sample Final A, Question 20

Question Consider the following rational function,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = x^2} does not have an inverse.
d) True. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cos^2(x) - cos(x) = 0} has multiple solutions.
e) True.
f) False.