Let's evaluate the function [tex]\( f(x) = 6 e^x \)[/tex] at the specified points. We'll calculate [tex]\( f(-3) \)[/tex], [tex]\( f(-1) \)[/tex], [tex]\( f(0) \)[/tex], [tex]\( f(1) \)[/tex], and [tex]\( f(3) \)[/tex] and round the results to two decimal places.
1. Evaluate [tex]\( f(-3) \)[/tex]:
[tex]\[
f(-3) = 6 e^{-3}
\][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[
f(-3) \approx 0.30
\][/tex]
2. Evaluate [tex]\( f(-1) \)[/tex]:
[tex]\[
f(-1) = 6 e^{-1}
\][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[
f(-1) \approx 2.21
\][/tex]
3. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 6 e^{0}
\][/tex]
Since [tex]\( e^0 = 1 \)[/tex], we have:
[tex]\[
f(0) = 6 \cdot 1 = 6.00
\][/tex]
4. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 6 e^{1}
\][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[
f(1) \approx 16.31
\][/tex]
5. Evaluate [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = 6 e^{3}
\][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[
f(3) \approx 120.51
\][/tex]
The evaluated values of the function at the given points are:
[tex]\[
\begin{align*}
f(-3) & \approx 0.30, \\
f(-1) & \approx 2.21, \\
f(0) & = 6.00, \\
f(1) & \approx 16.31, \\
f(3) & \approx 120.51.
\end{align*}
\][/tex]
