which equation is represented by the graph below?\no y = ln x - 3\no y = ln x - 4\no y = e^x - 3

Answer:

C. $y = e^{x}-3$

Explanation:

Step1: Analyze domain of $\ln x$ functions

The functions $y=\ln x - 3$ and $y=\ln x - 4$ have domain $x>0$. But the given graph has points for $x < 0$, so these can't be correct.

Step2: Analyze $y = e^{x}-3$

The general form of the exponential - function is $y = a\cdot e^{x}+k$. For $y = e^{x}-3$, when $x = 0$, $y=e^{0}-3=1 - 3=-2$. Also, as $x\to-\infty$, $y = e^{x}-3\to - 3$ (since $\lim_{x\to-\infty}e^{x}=0$), and as $x\to+\infty$, $y = e^{x}-3\to+\infty$, which matches the given graph.