Consider the following graph of the function *g*.
The *x* *y*-coordinate plane is given. A function composed of 5 parts is on the graph.

The first part is a curve that starts at a closed point in the second quadrant at *x* = −3, goes down and right becoming more steep, passes through an open point at *x* = −2, crosses the *x*-axis near *x* = −1.4, and exits the window almost vertically just to the left of *x* = −1.

The second part is a curve that enters the window almost vertically just to the right of *x* = −1, goes up and right becoming less steep, crosses the *x*-axis near *x* = −0.8, and ends at a closed point on the positive *y*-axis.

The third part is a curve that starts at an open point on the negative *y*-axis, goes down and right becoming more steep, and ends at an open point at *x* = 1.

The fourth part is a point that lies directly above the end of the third part in the fourth quadrant at *x* = 1.

The fifth part is a curve that starts at an open point directly above the fourth part in the first quadrant at *x* = 1, goes up and right becoming more steep, and ends at a closed point at *x* = 3.

From the given graph of *g*, state the numbers at which *g* is discontinuous. (Enter your answers as a comma-separated list.)

To determine where the function \( g(x) \) is discontinuous, we need to identify points on the graph where there are breaks, jumps, or asymptotes. A function is discontinuous at a point if it is not defined at that point, if there is a jump between the left-hand limit and right-hand limit, or if it tends to infinity.

### Analysis of the Graph Parts:

1. **First Part**:
   - The curve starts at a closed point at \( x = -3 \) and goes downward and right, becoming steeper, until it reaches an open point at \( x = -2 \).
   - At \( x = -2 \), there is a discontinuity because the point is open (the function is not defined there).

2. **Second Part**:
   - The curve enters the graph window just right of \( x = -1 \) and ends at a closed point on the positive \( y \)-axis.
   - As the first part of the curve leaves near \( x = -1 \), and the second part enters immediately after, this indicates a **vertical asymptote** at \( x = -1 \). Therefore, \( x = -1 \) is also a point of discontinuity.

3. **Third Part**:
   - The curve starts from an open point on the negative \( y \)-axis and ends at an open point at \( x = 1 \).
   - At \( x = 1 \), there is another discontinuity since it ends at an open point.

4. **Fourth Part**:
   - There is a separate point plotted directly above the end of the third part at \( x = 1 \) in the fourth quadrant. 
   - Since the curve doesn't connect to this point smoothly, \( x = 1 \) remains a discontinuity.

5. **Fifth Part**:
   - The curve starts again in the first quadrant from an open point above the point in the fourth quadrant at \( x = 1 \) and ends at a closed point at \( x = 3 \).
   - The function is defined continuously on this part, so there is no new discontinuity here.

### Conclusion:

The function \( g(x) \) is discontinuous at the points:

- \( x = -2 \) (open point, function not defined)
- \( x = -1 \) (vertical asymptote)
- \( x = 1 \) (jump discontinuity)

### Final Answer:

The points at which \( g(x) \) is discontinuous are:

\[
\boxed{-2, -1, 1}
\]

Would you like more details on the types of discontinuities or have any other questions?

### Relative Questions to Explore Further:
1. What are the different types of discontinuities in a function?
2. How do you determine if a discontinuity is removable or non-removable?
3. What is the difference between a jump discontinuity and an infinite discontinuity?
4. How can you use limits to describe the continuity of a function at a point?
5. What are the implications of discontinuities in real-world applications?

**Tip**: Always check for open and closed points on a graph, as they indicate whether a function is defined or not at a particular point.

Consider the following graph of the function *g*. The *x* *y*-coordinate plane is given. A function composed of 5 parts is on the graph. The first part is a curve that starts at a closed point in the second quadrant at *x* = −3, goes down and right becoming more steep, passes through an open point at *x* = −2, crosses the *x*-axis near *x* = −1.4, and exits the window almost vertically just to the left of *x* = −1. The second part is a curve that enters the window almost vertically just to the right of *x* = −1, goes up and right becoming less steep, crosses the *x*-axis near *x* = −0.8, and ends at a closed point on the positive *y*-axis. The third part is a curve that starts at an open point on the negative *y*-axis, goes down and right becoming more steep, and ends at an open point at *x* = 1. The fourth part is a point that lies directly above the end of the third part in the fourth quadrant at *x* = 1. The fifth part is a curve that starts at an open point directly above the fourth part in the first quadrant at *x* = 1, goes up and right becoming more steep, and ends at a closed point at *x* = 3. From the given graph of *g*, state the numbers at which *g* is discontinuous. (Enter your answers as a comma-separated list.)

Learn how to identify points of discontinuity on a piecewise function graph. This detailed breakdown explains key concepts such as vertical asymptotes and jump discontinuities, and is suitable for students in Grades 10-12.

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