Question

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

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

Explanation:

Step1: Analyze the range of \(y = e^{x}\)

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

Step2: Analyze the range of \(y=e^{x}+2\)

If \(y = e^{x}+2\), and we know that \(e^{x}>0\), then by adding 2 to each part of the inequality \(e^{x}>0\), we get \(e^{x}+2>0 + 2\).

Answer:

\((2,\infty)\)