Given 
g(x) = 2^x + 1,
 evaluate the following.
(a)    g(3)
 



(b)    g(2)
 



(c)    g(-2)

Given the function \( g(x) = 2^x + 1 \), we can evaluate it at the specified values:

### (a) \( g(3) \)
\[
g(3) = 2^3 + 1 = 8 + 1 = 9
\]

### (b) \( g(2) \)
\[
g(2) = 2^2 + 1 = 4 + 1 = 5
\]

### (c) \( g(-2) \)
\[
g(-2) = 2^{-2} + 1 = \frac{1}{2^2} + 1 = \frac{1}{4} + 1 = 1.25
\]

Thus, the results are:
- \( g(3) = 9 \)
- \( g(2) = 5 \)
- \( g(-2) = 1.25 \)

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What is the general behavior of \( g(x) \) as \( x \) increases or decreases?
2. How would you calculate \( g(x) \) for fractional values of \( x \)?
3. What is the inverse of \( g(x) \), if it exists?
4. How does \( g(x) \) compare to other exponential functions, like \( g(x) = 3^x + 1 \)?
5. Can you graph \( g(x) = 2^x + 1 \) and describe its shape?

**Tip**: For negative exponents, \( 2^{-x} = \frac{1}{2^x} \), which makes the function decrease as \( x \) becomes more negative.

Given g(x) = 2^x + 1, evaluate the following: (a) g(3), (b) g(2), (c) g(-2).

Learn how to evaluate the exponential function g(x) = 2^x + 1 at specific values of x. This example covers the calculations for g(3), g(2), and g(-2), providing detailed solutions. Suitable for students in Grades 9-11 studying exponential functions.

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