Question

1. (14 points) let f(x)=e^x + 2

(a) (2 points) find the range of f. write your answer in interval notation.
write your answer using interval notation:
range of f(x):
(b) (4 points) graph f on the grid below. label the horizontal asymptote and intercepts on your graph.

Explanation:

Step1: Recall the range of the exponential function

The exponential function $y = e^{x}$ has a range of $(0,\infty)$. That is, $e^{x}>0$ for all real - valued $x$.

Step2: Find the range of $f(x)=e^{x}+2$

If $y = e^{x}$ and $f(x)=y + 2$, then by adding 2 to each value in the range of $e^{x}$, we get the range of $f(x)$. If $e^{x}>0$, then $e^{x}+2>2$. So the range of $f(x)$ is $(2,\infty)$.

Answer:

$(2,\infty)$