Determine which of the following is not true for the graph of $f ( x ) = \frac { 2 x ^ { 2 } + x - 1 } { x ^ { 2 } - 1 }$
A)ƒ has no relative maximum.
B)ƒ has no relative minimum.
C)ƒ has a vertical asymptote: x = 1.
D)ƒ has a horizontal asymptote: y = 2.
E)ƒ is concave downward on $( 1 , \infty ) .$

Question

Determine which of the following is not true for the graph of $f ( x ) = \frac { 2 x ^ { 2 } + x - 1 } { x ^ { 2 } - 1 }$ 
A)ƒ has no relative maximum.
B)ƒ has no relative minimum.
C)ƒ has a vertical asymptote: x = 1.
D)ƒ has a horizontal asymptote: y = 2.
E)ƒ is concave downward on $( 1 , \infty ) .$

Quizplus · Accepted Answer

The graph of $f(x) = \frac{2x^2 + x - 1}{x^2 - 1}$ simplifies to $f(x) = 2 + \frac{x}{x^2 - 1}$, which shows that as $x$ approaches infinity, the function approaches the horizontal asymptote $y = 2$, not exhibiting a concave downward behavior on $(1, \infty)$.

Determine Which of the Following Is Not True for the Graph