https://file.aiquickdraw.com/mathbot/file/1729050304622rslj7xc6.jpg

The function provided is \( f(x) = 3^x + x \), and we are asked to find the values for \( f(-2) \), \( f(0) \), and \( f(3) \).

### Step-by-step solutions:

1. **For \( f(-2) \):**
   \[
   f(-2) = 3^{-2} + (-2)
   \]
   \[
   3^{-2} = \frac{1}{3^2} = \frac{1}{9}
   \]
   So,
   \[
   f(-2) = \frac{1}{9} - 2 = \frac{1}{9} - \frac{18}{9} = \frac{-17}{9}
   \]
   Therefore, \( f(-2) = \frac{-17}{9} \).

2. **For \( f(0) \):**
   \[
   f(0) = 3^0 + 0 = 1 + 0 = 1
   \]
   Therefore, \( f(0) = 1 \).

3. **For \( f(3) \):**
   \[
   f(3) = 3^3 + 3 = 27 + 3 = 30
   \]
   Therefore, \( f(3) = 30 \).

### Summary of the values:
- \( f(-2) = \frac{-17}{9} \)
- \( f(0) = 1 \)
- \( f(3) = 30 \)

You can now place these values into the corresponding boxes.

Do you need more details on the calculations or any further explanation?

### 5 Related Questions:
1. How do you evaluate exponential functions for negative exponents?
2. What are the properties of exponents that help simplify expressions like \( 3^{-2} \)?
3. How would the function change if the exponent had a variable like \( x^2 \)?
4. Can the function \( f(x) = 3^x + x \) ever be undefined? Why or why not?
5. How do we determine the asymptotic behavior of exponential functions as \( x \) approaches infinity?

### Tip:
Always check whether the base of an exponent is positive or negative, as it can change the overall result when raising to negative powers.

Find the function values for f(-2), f(0), and f(3). The function is f(x) = 3^x + x.

Learn how to evaluate the function f(x) = 3^x + x at specific points like f(-2), f(0), and f(3). This example includes solving for negative exponents, exponent properties, and substitution methods. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation