Which statement describes the behavior of the function f (x) = StartFraction 3 x Over 4 minus x EndFraction?

First Method: Using Graph

Finding the limits as x approaches infinity and negative infinity is one way to solve this problem. As x reaches infinity, simply follow the graph line (colored purple) to the far right to find its limit. If we trace it, we can see that the Y value never exceeds -3 (orange), indicating that the limit is equal to -3 as x approaches infinity. You'd do the same with negative infinity, the limit is -3. We may now say the following:

And that's the answer to your question.

Second Method: Using Mathematics

I'm not sure if this solution is suitable for your stage, but you can solve this problem using L'Hopital's rule:

Graphed by: Desmos

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.