Supply a valid technology formula for the given function.
f(x) = 2^x
f(x) =
Compute the missing values as indicated in the table below.
x	−3	−2	−1	0	1	2	3
f(x)

The given function is \( f(x) = 2^x \). To compute the missing values for each \( x \) value, we simply substitute \( x \) into the function \( f(x) = 2^x \) and calculate the corresponding \( f(x) \).

Here are the computations:

- For \( x = -3 \): 
  \[
  f(-3) = 2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125
  \]
- For \( x = -2 \): 
  \[
  f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25
  \]
- For \( x = -1 \): 
  \[
  f(-1) = 2^{-1} = \frac{1}{2} = 0.5
  \]
- For \( x = 0 \): 
  \[
  f(0) = 2^0 = 1
  \]
- For \( x = 1 \): 
  \[
  f(1) = 2^1 = 2
  \]
- For \( x = 2 \): 
  \[
  f(2) = 2^2 = 4
  \]
- For \( x = 3 \): 
  \[
  f(3) = 2^3 = 8
  \]

Thus, the completed table is:

\[
\begin{array}{c|c}
x & f(x) \\
\hline
-3 & 0.125 \\
-2 & 0.25 \\
-1 & 0.5 \\
0 & 1 \\
1 & 2 \\
2 & 4 \\
3 & 8 \\
\end{array}
\]

Would you like more details or have any questions about this?

### Related Questions:
1. How do we calculate negative exponents in general?
2. What is the effect of different bases in exponential functions?
3. How do exponential functions compare to linear functions?
4. What happens to the function as \( x \to -\infty \) and \( x \to \infty \)?
5. How can exponential functions model real-world scenarios like population growth?

### Tip:
When \( x = 0 \), any non-zero base raised to the power of 0 is always 1 (i.e., \( a^0 = 1 \) for any \( a \neq 0 \)).

Supply a valid technology formula for the given function. f(x) = 2^x. Compute the missing values as indicated in the table below. x −3 −2 −1 0 1 2 3 f(x)

Learn how to compute values for the exponential function f(x) = 2^x across negative and positive x values. This example covers key concepts like negative exponents, powers of 2, and the laws of exponents. Suitable for students in Grades 8-10.

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