Determine the value that $f ( x ) = \frac { 3 x - 5 } { x - 6 }$ approaches as $x$ increases and decreases in magnitude without bound.
A) 6
B) 5
C) 4
D) 3
E) 2

Question

Quizplus · Accepted Answer

As $x$ increases or decreases without bound, the value of $f(x) = \frac{3x - 5}{x - 6}$ approaches the coefficient of $x$ in the numerator divided by the coefficient of $x$ in the denominator, which is $\frac{3}{1} = 3$. This is because the terms not multiplied by $x$ become negligible in comparison to the terms multiplied by $x$ as $x$ approaches infinity or negative infinity.

Determine the Value That f(x)=3x−5x−6f ( x ) = \frac { 3 x - 5 } { x - 6 }f(x)=x−63x−5​

Determine the Value That $f ( x ) = \frac { 3 x - 5 } { x - 6 }$