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The given function is \( f(x) = 4e^{-0.6x} \). We are asked to calculate values of \( f(x) \) for specific values of \( x \), and then identify the correct graph from the options provided.

### Step 1: Compute the values of \( f(x) \) at the specified points:
- For \( x = -2 \):
  \[
  f(-2) = 4e^{-0.6(-2)} = 4e^{1.2} \approx 4 \times 3.3201 \approx 13.280
  \]

- For \( x = -1 \):
  \[
  f(-1) = 4e^{-0.6(-1)} = 4e^{0.6} \approx 4 \times 1.8221 \approx 7.288
  \]

- For \( x = 0 \):
  \[
  f(0) = 4e^{-0.6(0)} = 4e^0 = 4
  \]

- For \( x = 1 \):
  \[
  f(1) = 4e^{-0.6(1)} = 4e^{-0.6} \approx 4 \times 0.5488 \approx 2.195
  \]

- For \( x = 2 \):
  \[
  f(2) = 4e^{-0.6(2)} = 4e^{-1.2} \approx 4 \times 0.3012 \approx 1.205
  \]

Thus, the table of values is:
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-2 & 13.280 \\
-1 & 7.288 \\
0 & 4 \\
1 & 2.195 \\
2 & 1.205 \\
\end{array}
\]

### Step 2: Choose the correct graph.
The function \( f(x) = 4e^{-0.6x} \) is an exponential decay function, starting from a high value and decreasing as \( x \) increases. Based on the characteristics:
- The function is always positive (since the exponential function never reaches zero or becomes negative).
- As \( x \to \infty \), \( f(x) \) approaches zero.
- As \( x \to -\infty \), \( f(x) \) grows rapidly towards infinity.

Looking at the options, the correct graph is the one in the bottom right, showing exponential decay as \( x \) increases and rapid growth as \( x \) becomes negative.

Would you like to see more details or have any questions? Here are five related questions:

1. How do we interpret the rate of decay from the exponent \( -0.6x \)?
2. What happens to the graph if we increase the decay constant (e.g., make it \( -0.8x \))?
3. How would the graph change if the coefficient \( 4 \) were larger or smaller?
4. How do exponential functions differ from polynomial or linear functions in behavior?
5. What real-life phenomena can be modeled using exponential decay functions?

**Tip:** Exponential functions, like \( e^{-kx} \), decay faster as the constant \( k \) increases.

Use a graphing utility to construct a table of values for the function f(x) = 4e^(-0.6x) and sketch the graph of the function.

Learn how to construct a table of values and identify the graph for the exponential decay function f(x) = 4e^(-0.6x). This problem involves calculating specific values for x and understanding the behavior of exponential decay. Suitable for high school students in Grades 10-12.

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