https://file.aiquickdraw.com/mathbot/file/1726929154954o24ohuv4.jpg

The function given in the image is a piecewise function:

\[
g(x) =
\begin{cases}
x^2, & \text{if } x \leq -1 \\
x + 5, & \text{if } x > -1
\end{cases}
\]

We are asked to find the values of \( g(-3) \), \( g(-1) \), \( g(0) \), and \( g(2) \).

### Solution:
1. **\( g(-3) \)**:
   Since \( -3 \leq -1 \), we use the first part of the piecewise function: 
   \[
   g(-3) = (-3)^2 = 9
   \]

2. **\( g(-1) \)**:
   Since \( -1 \leq -1 \), we again use the first part of the piecewise function: 
   \[
   g(-1) = (-1)^2 = 1
   \]

3. **\( g(0) \)**:
   Since \( 0 > -1 \), we use the second part of the piecewise function: 
   \[
   g(0) = 0 + 5 = 5
   \]

4. **\( g(2) \)**:
   Since \( 2 > -1 \), we use the second part of the piecewise function:
   \[
   g(2) = 2 + 5 = 7
   \]

### Final Answers:
- \( g(-3) = 9 \)
- \( g(-1) = 1 \)
- \( g(0) = 5 \)
- \( g(2) = 7 \)

Do you want further details on how piecewise functions work? 

Here are some related questions to explore:
1. What are the general properties of piecewise functions?
2. How do you graph a piecewise function?
3. Can a piecewise function have more than two conditions?
4. How do you find the domain and range of a piecewise function?
5. What is the significance of continuity in piecewise functions?

**Tip:** When evaluating piecewise functions, always pay close attention to the conditions that specify the intervals for different expressions.

Дано функцію g(x) = { x^2, якщо x ≤ -1; x + 5, якщо x > -1 }. Знайдіть g(-3); g(-1); g(0); g(2).

Learn how to solve a piecewise function, where one part is quadratic (x^2) and the other is linear (x + 5). This problem demonstrates how to evaluate the function for specific values: g(-3), g(-1), g(0), and g(2).

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