Determine the function values, if possible. Express all numbers as integers or simplified fractions. Select "Undefined" if applicable. $$ f(x)=\frac{4}{x+2} $$

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To determine the function values for $$ f(x) = \frac{4}{x + 2} $$, we'll evaluate the function for specific values of $$ x $$. However, since no specific $$ x $$-values were provided, I'll outline the general approach and highlight important points about the function.

### **Understanding the Function $$ f(x) = \frac{4}{x + 2} $$**

1. **Domain of the Function:**
   - The function is defined for all real numbers except where the denominator is zero.
   - Set the denominator equal to zero and solve for $$ x $$:
     $$
     x + 2 = 0 \quad \Rightarrow \quad x = -2
     $$
   - **Domain:** All real numbers $$ \mathbb{R} $$ except $$ x = -2 $$.
   - **Undefined Point:** $$ x = -2 $$ (At this point, the function is **Undefined**).

2. **Evaluating $$ f(x) $$ for Specific Values:**
   - **Example 1:** $$ x = 0 $$
     $$
     f(0) = \frac{4}{0 + 2} = \frac{4}{2} = 2
     $$
   - **Example 2:** $$ x = 1 $$
     $$
     f(1) = \frac{4}{1 + 2} = \frac{4}{3}
     $$
   - **Example 3:** $$ x = -3 $$
     $$
     f(-3) = \frac{4}{-3 + 2} = \frac{4}{-1} = -4
     $$
   - **Example 4:** $$ x = -2 $$
     $$
     f(-2) = \frac{4}{-2 + 2} = \frac{4}{0} \quad \text{(Undefined)}
     $$

3. **Summary of Function Values:**

| $$ x $$ | $$ f(x) $$         |
|---------|--------------------|
| 0       | $$ 2 $$            |
| 1       | $$ \frac{4}{3} $$  |
| -3      | $$ -4 $$           |
| -2      | **Undefined**     |

### **Key Points to Remember:**

- **Undefined Point:** $$ x = -2 $$ makes the denominator zero, rendering $$ f(x) $$ undefined.
- **Simplified Fractions:** Ensure that all fractions are simplified. For example, $$ \frac{4}{2} = 2 $$ and $$ \frac{4}{3} $$ is already in its simplest form.
- **Expressing as Integers or Simplified Fractions:** Always simplify the function values as much as possible unless the result is undefined.

If you have specific $$ x $$-values you'd like to evaluate, feel free to provide them, and I can calculate the corresponding $$ f(x) $$ values for you!
The function $$ f(x) = \frac{4}{x + 2} $$ is defined for all real numbers except $$ x = -2 $$, where it is undefined. For other values of $$ x $$, the function can be evaluated as follows: - $$ f(0) = 2 $$ - $$ f(1) = \frac{4}{3} $$ - $$ f(-3) = -4 $$ - $$ f(-2) $$ is **Undefined** Ensure to simplify all fractions and express the results as integers or simplified fractions.

Determine the function values, if possible. Express all numbers as integers or simplified fractions. Select "Undefined" if applicable. \[ f(x)=\frac{4}{x+2} \]

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