3. (14 points) let ( f(x)=e^{x}+2 ) (a) (2 points) find the range of ( f ). write your answer in interval…

3. (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 inter cepts on your graph.

3. (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 inter cepts on your graph.

Answer

Explanation:

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

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

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

If (y = e^{x}+2), and (e^{x}>0), then (y=e^{x}+2>0 + 2).

Answer:

((2,\infty))