Determine the value that the function f approaches as the magnitude of x increases.
$f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$
A)0
B) $- \frac { 1 } { 2 }$
C)-1
D)8
E) $- \frac { 1 } { 5 }$

Question

Determine the value that the function f approaches as the magnitude of x increases. 
$f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$  
A)0
B) $- \frac { 1 } { 2 }$
C)-1
D)8
E) $- \frac { 1 } { 5 }$

Quizplus · Accepted Answer

As the magnitude of $x$ increases, the term $8x - 1$ in the numerator grows linearly, while the term $x^2 + 2$ in the denominator grows quadratically. The quadratic growth in the denominator outpaces the linear growth in the numerator, causing the value of the function to approach 0.

Determine the Value That the Function F Approaches as the Magnitude