Determine the value that the function f approaches as the magnitude of x increases.
$f ( x ) = 3 + \frac { 1 } { x - 4 }$
A)2.75
B) 3
C) 1
D) 4
E)-0.25

Question

Determine the value that the function f approaches as the magnitude of x increases. 
 $f ( x ) = 3 + \frac { 1 } { x - 4 }$  
A)2.75
B) 3
C) 1
D) 4
E)-0.25

Quizplus · Accepted Answer

As the magnitude of $x$ increases, the term $\frac{1}{x-4}$ approaches 0 because the denominator becomes very large in magnitude, making the fraction itself very small. Therefore, the value that $f(x)$ approaches is simply the constant term, which is 3.

Determine the Value That the Function F Approaches as the Magnitude