Question
Question content area top
Part 1
Graph the given function by making a table of coordinates.
f left parenthesis x right parenthesis equals 3 Superscript x
Question content area bottom
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.)
Part 1
Graph the given function by making a table of coordinates.
f left parenthesis x right parenthesis equals 3 Superscript x
Question content area bottom
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!
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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