y = 2e^x - 1\nchoose the correct graph below.\nhelp me solve this view an example get more help \nclear all

Explanation:

Step1: Analyze the function at $x = 1$

When $x = 1$, $y=2e^{1 - 1}=2e^{0}=2\times1 = 2$.

Step2: Analyze the behavior as $x\to-\infty$

As $x\to-\infty$, $e^{x - 1}\to0$, so $y = 2e^{x - 1}\to0$.

Step3: Analyze the general form of exponential - type function

The function $y = 2e^{x - 1}$ is an exponential function of the form $y = ae^{x - h}$, where $a = 2$ and $h = 1$, and exponential functions of the form $y = ae^{x - h}$ with $a>0$ are increasing functions.

We look for a graph that passes through the point $(1,2)$, approaches the $x$ - axis as $x\to-\infty$ and is an increasing function.

Answer:

(Without seeing the actual graphs, we can't give a specific option. But the correct graph should have the above - mentioned characteristics. If you can describe the graphs in more detail, we can further determine the answer.)