Question

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Part 1
Graph the given function by making a table of coordinates.
f left parenthesis x right parenthesis equals 3 Superscript x
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Part 1
Complete the table of coordinates.
x
minus2
minus1
0
1
2
y
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
​(Type integers or fractions. Simplify your​ answers.)

Answers

Answered by GPT-4o mini
To create a table of coordinates for the function \( f(x) = 3^x \), we will calculate the value of the function for each designated \( x \) value. Here's how you can do it for the provided \( x \) values: -2, -1, 0, 1, 2.

1. **For \( x = -2 \):**
\[
f(-2) = 3^{-2} = \frac{1}{3^2} = \frac{1}{9}
\]

2. **For \( x = -1 \):**
\[
f(-1) = 3^{-1} = \frac{1}{3}
\]

3. **For \( x = 0 \):**
\[
f(0) = 3^0 = 1
\]

4. **For \( x = 1 \):**
\[
f(1) = 3^1 = 3
\]

5. **For \( x = 2 \):**
\[
f(2) = 3^2 = 9
\]

Now we can fill out the table:

| \( x \) | \( y = f(x) \) |
|:-----------:|:------------------:|
| -2 | \( \frac{1}{9} \) |
| -1 | \( \frac{1}{3} \) |
| 0 | \( 1 \) |
| 1 | \( 3 \) |
| 2 | \( 9 \) |

### Summary of the Coordinates:
- \( (-2, \frac{1}{9}) \)
- \( (-1, \frac{1}{3}) \)
- \( (0, 1) \)
- \( (1, 3) \)
- \( (2, 9) \)

You can now use these calculations to plot the function on a graph!
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