Question

evaluate $y = e^x + 1$ for the following values of $x$. round to the nearest thousandth.\
$x = -2, y \approx \boldsymbol{1.135}$ $x = 1, y \approx \boldsymbol{3.718}$ $x = 2, y \approx \boldsymbol{8.389}$\
complete\
which of the following is the graph of $y = e^x + 1$?

Explanation:

Step1: Identify base function behavior

The base function is $y=e^x$, which is an exponential growth function (increasing for all $x$, passes through $(0,1)$).

Step2: Apply vertical shift

The given function is $y=e^x + 1$, which shifts $y=e^x$ up by 1 unit. So it passes through $(0, 1+1)=(0,2)$, and still increases as $x$ increases.

Step3: Match with calculated points

From the first part:

• When $x=-2$, $y\approx1.135$ (positive, near 1)
• When $x=1$, $y\approx3.718$
• When $x=2$, $y\approx8.389$

These points correspond to an increasing curve that starts near the x-axis for negative $x$, passes through $(0,2)$, and rises steeply for positive $x$.

Answer:

The correct graph is the second one (the middle graph, which shows an increasing exponential curve passing near $(0,2)$, rising steeply for positive $x$, and approaching the x-axis from above for negative $x$).