https://file.aiquickdraw.com/mathbot/file/1730145336711hzkxi585.jpg

The problem defines the function \( f(x) = 2^x \) and asks to find \( f(x) \) for each given value of \( x \) in the table.

Let's calculate \( f(x) \) for each value of \( x \) in the table:

1. When \( x = -3 \):
   \[
   f(-3) = 2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125
   \]

2. When \( x = -2 \):
   \[
   f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25
   \]

3. When \( x = -1 \):
   \[
   f(-1) = 2^{-1} = \frac{1}{2} = 0.5
   \]

4. When \( x = 0 \):
   \[
   f(0) = 2^0 = 1
   \]

5. When \( x = 1 \):
   \[
   f(1) = 2^1 = 2
   \]

The completed table should look like this:

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

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How would the values change if \( f(x) = 3^x \) instead?
2. What happens to \( f(x) \) as \( x \) approaches very large positive values?
3. What is the behavior of \( f(x) \) as \( x \) approaches very large negative values?
4. How does the function \( f(x) = 2^x \) compare to \( g(x) = 10^x \)?
5. What would \( f(x) \) be for non-integer values of \( x \), such as \( x = 0.5 \)?

**Tip:** In exponential functions, as \( x \) increases, \( f(x) = 2^x \) grows very quickly, while it approaches zero as \( x \) decreases.

La función f está definida por la regla f(x) = 2^x. Hallar f(x) para cada valor de x en la tabla.

Learn how to find f(x) values for each x in an exponential function defined by f(x) = 2^x. This exercise involves evaluating the function at different x values, with results such as f(-3) = 0.125 and f(1) = 2. Perfect for students in Grades 7-9.

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