Answer:
The graph approaches –3 as x approaches infinity. Option a is correct.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{3x}{4-x} [/tex]
We have to find value of function as x approaches infinity. Take limit both sides as x approaches to infinity.
[tex]\lim_{x\rightarrow \infty}f(x)=\lim_{x\rightarrow \infty}\frac{3x}{4-x}[/tex]
Taking x common from the denominator.
[tex]\lim_{x\rightarrow \infty}f(x)=\lim_{x\rightarrow \infty}\frac{3x}{x(\frac{4}{x}-1)}[/tex]
Cancel out common factor x.
[tex]\lim_{x\rightarrow \infty}f(x)=\lim_{x\rightarrow \infty}\frac{3}{\frac{4}{x}-1}[/tex]
Apply limits.
[tex]\lim_{x\rightarrow \infty}f(x)=\frac{3}{\frac{4}{\infty}-1}[/tex]
[tex]\lim_{x\rightarrow \infty}f(x)=\frac{3}{0-1}[/tex]
[tex]\lim_{x\rightarrow \infty}f(x)=-3[/tex]
Therefore the graph approaches –3 as x approaches infinity.
