Question

graph the equation by completing the table and plotting points. identify the domain.
$y = e^x + 3$
part 1 of 3
complete the table. round to two decimal places when necessary.

x	y
-4	3.02
-3	3.05
-2	3.14
-1	3.37
0	4.00
1	5.72

alternate answer:

x	y
-4	3.02
-3	3.05
-2	3.14
-1	3.37
0	4
1	5.72

part: 1 / 3
part 2 of 3
graph the equation. plot the horizontal asymptote and the points from the table.

Explanation:

Step1: Analyze the function type

The function is \( y = e^x + 3 \), which is an exponential function. The base of the exponential function \( e^x \) is \( e \) (Euler's number, approximately 2.718), and exponential functions of the form \( y = a^x \) (where \( a>0, a
eq1 \)) have a domain of all real numbers because you can raise \( a \) to any real - valued power.

Step2: Determine the domain of \( y = e^x+3 \)

For the function \( y = e^x+3 \), the term \( e^x \) is defined for all real numbers \( x \). When we add 3 to \( e^x \), the domain does not change because adding a constant to a function does not restrict the values of \( x \) for which the function is defined. So, the domain of the function \( y = e^x + 3 \) is all real numbers. In interval notation, the domain is \( (-\infty, \infty) \).

Answer:

The domain of the function \( y = e^x+3 \) is all real numbers, or in interval notation \( (-\infty, \infty) \)