To complete the table of coordinates for the function \( f(x) = 2^x \), we will calculate \( f(x) \) for the given \( x \) values: -2, -1, 0, 1, and 2.
Let's calculate the values of \( y \):
-
When \( x = -2 \): \[ f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \]
-
When \( x = -1 \): \[ f(-1) = 2^{-1} = \frac{1}{2^1} = \frac{1}{2} \]
-
When \( x = 0 \): \[ f(0) = 2^0 = 1 \]
-
When \( x = 1 \): \[ f(1) = 2^1 = 2 \]
-
When \( x = 2 \): \[ f(2) = 2^2 = 4 \]
Now, we can fill in the table with the calculated values of \( y \):
| \( x \) | \( y = f(x) \) | |-----------|------------------| | -2 | \( \frac{1}{4} \) | | -1 | \( \frac{1}{2} \) | | 0 | 1 | | 1 | 2 | | 2 | 4 |
Complete Table of Coordinates:
- \( (-2, \frac{1}{4}) \)
- \( (-1, \frac{1}{2}) \)
- \( (0, 1) \)
- \( (1, 2) \)
- \( (2, 4) \)
You can now use these coordinates to graph the function \( f(x) = 2^x \).