Question

which of the following shows the graph of $y = 2e^x$?

Explanation:

Step1: Find y-intercept (x=0)

$y=2e^{0}=2\times1=2$

Step2: Analyze function behavior

As $x\to+\infty$, $y=2e^x\to+\infty$; as $x\to-\infty$, $y=2e^x\to0^+$

Step3: Match with given graphs

The top graph has y-intercept near 2, approaches 0 as $x\to-\infty$, and increases to $+\infty$ as $x\to+\infty$, which matches.

Answer:

The top graph (the one with the red curve starting near (0,2), approaching 0 as x goes to negative infinity, and increasing towards positive infinity as x goes to positive infinity) is the graph of $y=2e^x$.