for the function $f(x)=2e^{x + 2}$, calculate the following function values. round to 4 decimal…

Explanation:

Step1: Calculate (f(-3))

Substitute (x = - 3) into (f(x)=2e^{x + 2}). [ \begin{align*} f(-3)&=2e^{-3 + 2}\ &=2e^{-1}\ &=\frac{2}{e}\ &\approx\frac{2}{2.7183}\ &\approx0.7358 \end{align*} ]

Step2: Calculate (f(-1))

Substitute (x=-1) into (f(x) = 2e^{x + 2}). [ \begin{align*} f(-1)&=2e^{-1+2}\ &=2e^{1}\ &=2\times2.7183\ &\approx5.4366 \end{align*} ]

Step3: Calculate (f(0))

Substitute (x = 0) into (f(x)=2e^{x + 2}). [ \begin{align*} f(0)&=2e^{0+2}\ &=2e^{2}\ &=2\times7.3891\ &\approx14.7781 \end{align*} ]

Step4: Calculate (f(1))

Substitute (x = 1) into (f(x)=2e^{x + 2}). [ \begin{align*} f(1)&=2e^{1+2}\ &=2e^{3}\ &=2\times20.0855\ &\approx40.1710 \end{align*} ]

Step5: Calculate (f(3))

Substitute (x = 3) into (f(x)=2e^{x + 2}). [ \begin{align*} f(3)&=2e^{3+2}\ &=2e^{5}\ &=2\times148.4132\ &\approx296.8264 \end{align*} ]

Answer:

(f(-3)\approx0.7358) (f(-1)\approx5.4366) (f(0)\approx14.7781) (f(1)\approx40.1710) (f(3)\approx296.8264)