Determine which of the following is not true for the graph of $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 1 }$
A)ƒ has no relative maximum.
B)ƒ has no relative minimum.
C)ƒ has a vertical asymptote: x = 1.
D)ƒ has no horizontal asymptote.
E)ƒ is concave downward on $( - \infty , \infty )$

Question

Determine which of the following is not true for the graph of $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 1 }$ 
A)ƒ has no relative maximum.
B)ƒ has no relative minimum.
C)ƒ has a vertical asymptote: x = 1.
D)ƒ has no horizontal asymptote.
E)ƒ is concave downward on $( - \infty , \infty )$

Quizplus · Accepted Answer

The graph of $f(x) = \frac{x^2 - 9}{x - 1}$ simplifies to $f(x) = x + 1 + \frac{8}{x - 1}$ when factored and simplified. This shows that the function is not concave downward on all of $(- \infty, \infty)$ because the term $x + 1$ indicates a linear component that increases as $x$ increases, affecting the concavity of the function.

Determine Which of the Following Is Not True for the Graph