what is the value of $$ f\left(-2\right) $$ in the function $$ f\left(x\right)=2^{x} $$$$ +3 $$

The function is given as:

\[
f(x) = 2^x + 3
\]

To find $ f(-2) $, substitute $ x = -2 $ into the function:

\[
f(-2) = 2^{-2} + 3
\]

Since $ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} $, the expression becomes:

\[
f(-2) = \frac{1}{4} + 3
\]

Now, add the fractions:

\[
f(-2) = \frac{1}{4} + \frac{12}{4} = \frac{13}{4}
\]

Thus, the value of $ f(-2) $ is:

\[
f(-2) = \frac{13}{4} = 3.25
\]

### Do you have any questions, or would you like further details on the steps?

Here are 5 related questions:
1. What is the general form of exponential functions?
2. How would $ f(x) $ behave as $ x $ approaches infinity?
3. What is the derivative of $ f(x) = 2^x + 3 $?
4. How does the value of the base $ 2 $ affect the growth of the function?
5. What happens to the function $ f(x) $ as $ x $ becomes negative?

**Tip**: When evaluating powers of negative exponents, remember they represent fractions!

What is the value of f(-2) in the function f(x) = 2^x + 3?

Learn how to evaluate the function f(x) = 2^x + 3 at x = -2. This example demonstrates the application of exponential functions and exponent rules. Suitable for students in Grades 8-10, with a clear, step-by-step breakdown of the process.

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