https://file.aiquickdraw.com/mathbot/file/17253922953337pird7s6.jpg

To solve the questions based on the graph provided, I'll analyze the graph and determine the values of the function \( g(x) \) at the specified points.

1. **Reading the Graph:**
   - The graph shows a piecewise linear function \( g(x) \).
   - There are two line segments and one point of discontinuity at \( x = 1 \).
   - One segment extends from a negative slope (to the left of \( x = 1 \)), and the other has a positive slope (to the right of \( x = 1 \)).

2. **Determining the Values:**
   - **\( g(2) \):** Find where \( x = 2 \) intersects the graph. The corresponding \( y \)-value (or \( g(2) \)) is the function's value at that point.
   - **\( g(-3) \):** Similarly, find the intersection at \( x = -3 \) and determine the \( y \)-value.
   - **\( g(1^+) \):** This asks for the value of \( g(x) \) as \( x \) approaches 1 from the right (positive side).
   - **\( g(1^-) \):** This asks for the value of \( g(x) \) as \( x \) approaches 1 from the left (negative side).

Now, let’s calculate these values:

### a) \( g(2) \)
At \( x = 2 \), the graph intersects at \( y = -2 \).
- **\( g(2) = -2 \)**

### b) \( g(-3) \)
At \( x = -3 \), the graph intersects at \( y = 3 \).
- **\( g(-3) = 3 \)**

### c) \( g(1^-) \)
As \( x \) approaches 1 from the left, the graph reaches \( y = 4 \).
- **\( g(1^-) = 4 \)**

### d) \( g(1^+) \)
As \( x \) approaches 1 from the right, the graph reaches \( y = 0 \).
- **\( g(1^+) = 0 \)**

These are the answers to the questions based on the graph:

- **a) \( g(2) = -2 \)**
- **b) \( g(-3) = 3 \)**
- **c) \( g(1^-) = 4 \)**
- **d) \( g(1^+) = 0 \)**

Would you like further details or have any questions?

### Additional Questions:
1. What is the slope of the line segment for \( x < 1 \) on the graph?
2. What is the slope of the line segment for \( x > 1 \) on the graph?
3. How would you describe the behavior of \( g(x) \) as \( x \) approaches infinity?
4. What does the discontinuity at \( x = 1 \) indicate about the function?
5. How can you express \( g(x) \) as a piecewise function based on the graph?

### Tip:
When analyzing piecewise functions on a graph, always check for any discontinuities and understand the behavior of the function as it approaches these points from both sides.

Use the graph to find the following values: g(2), g(-3), g(1^-), g(1^+).

Determine the values of the function g(x) at specific points using a graph. This problem involves key concepts such as piecewise functions, continuity, and discontinuity, suitable for students in Grades 8-10.

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