Question

graph the equation by completing the table and plotting points. identify the domain. y = e^x + 5 part: 0 / 3 part 1 of 3 complete the table. round to two decimal places when necessary. x y -3 -2 -1 0 1 2

Explanation:

Step1: Calculate y when x = -3

Substitute \( x = -3 \) into \( y = e^x + 5 \). We know that \( e^{-3}=\frac{1}{e^3}\approx\frac{1}{20.0855}\approx0.0498 \). Then \( y = 0.0498 + 5 = 5.0498\approx5.05 \).

Step2: Calculate y when x = -2

Substitute \( x = -2 \) into \( y = e^x + 5 \). \( e^{-2}=\frac{1}{e^2}\approx\frac{1}{7.3891}\approx0.1353 \). Then \( y = 0.1353 + 5 = 5.1353\approx5.14 \).

Step3: Calculate y when x = -1

Substitute \( x = -1 \) into \( y = e^x + 5 \). \( e^{-1}=\frac{1}{e}\approx0.3679 \). Then \( y = 0.3679 + 5 = 5.3679\approx5.37 \).

Step4: Calculate y when x = 0

Substitute \( x = 0 \) into \( y = e^x + 5 \). \( e^{0}=1 \). Then \( y = 1 + 5 = 6 \).

Step5: Calculate y when x = 1

Substitute \( x = 1 \) into \( y = e^x + 5 \). \( e^{1}\approx2.7183 \). Then \( y = 2.7183 + 5 = 7.7183\approx7.72 \).

Step6: Calculate y when x = 2

Substitute \( x = 2 \) into \( y = e^x + 5 \). \( e^{2}\approx7.3891 \). Then \( y = 7.3891 + 5 = 12.3891\approx12.39 \).

Answer:

For \( x = -3 \), \( y\approx5.05 \); for \( x = -2 \), \( y\approx5.14 \); for \( x = -1 \), \( y\approx5.37 \); for \( x = 0 \), \( y = 6 \); for \( x = 1 \), \( y\approx7.72 \); for \( x = 2 \), \( y\approx12.39 \)

Filling the table:

\( x \)	\( y \)
-2	\( 5.14 \)
-1	\( 5.37 \)
0	\( 6 \)
1	\( 7.72 \)
2	\( 12.39 \)