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 $8x - 1$ grows linearly, while the term $x^2 + 2$ grows quadratically. The quadratic growth in the denominator dominates, making the fraction approach 0.

Determine the Value That the Function F Approaches as the Magnitude