Drawing the Graph: Analyzing Solutions and Questions

In summary, the electric field is discontinuous at x = 1 cm and x = 3 cm and is plotted without vertical lines to accurately represent the function's behavior. Drawing vertical lines would imply that the electric field has values in between the discontinuities, which it does not.
  • #1
ChiralSuperfields
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Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1673315233100.png
,
The solutions is,
1673315261826.png

However, why did they not draw vertical lines for the graph like this:
1673315340737.png
?

Thank you!
 
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  • #2
Callumnc1 said:
However, why did they not draw vertical lines for the graph like this:
Because the electric field is discontinuous at x = 1 cm and x = 3 cm and that is how discontinuous functions are plotted. Drawing a line as you suggest implies that the electric field has all the in-between values which it doesn't.
 
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  • #3
kuruman said:
Because the electric field is discontinuous at x = 1 cm and x = 3 cm and that is how discontinuous functions are plotted. Drawing a line as you suggest implies that the electric field has all the in-between values which it doesn't.
Got it, thank you @kuruman !
 

1. How do I draw a graph to analyze solutions?

To draw a graph for analyzing solutions, you will need to first determine the variables involved in the problem and their corresponding values. Then, plot these values on the x and y-axis of the graph. Finally, connect the points to create a line or curve, depending on the type of relationship between the variables. This will give you a visual representation of the solutions to the problem.

2. What are the key components of a graph for analyzing solutions?

The key components of a graph for analyzing solutions include a title, labeled x and y-axis, a scale, and a key or legend if needed. The title should accurately describe the problem being analyzed, while the x and y-axis should have appropriate labels and units. The scale should be evenly spaced and clearly indicate the increments used. The key or legend should explain the meaning of any symbols or colors used in the graph.

3. How can I determine the slope of a line on a graph?

The slope of a line on a graph can be determined by calculating the change in y over the change in x. This is also known as rise over run. To do this, select two points on the line and use the formula (y2 - y1) / (x2 - x1) to find the slope. The slope can also be determined by looking at the steepness of the line - a steeper line indicates a larger slope, while a flatter line indicates a smaller slope.

4. What is the difference between a linear and non-linear graph?

A linear graph is a straight line on a graph, indicating a constant relationship between the variables. This means that the change in one variable is directly proportional to the change in the other variable. On the other hand, a non-linear graph is a curved line on a graph, indicating a non-constant relationship between the variables. This means that the change in one variable is not directly proportional to the change in the other variable.

5. How can I use a graph to answer questions about a problem?

A graph can be used to answer questions about a problem by visually representing the relationship between the variables involved. By analyzing the shape, slope, and intercepts of the graph, you can determine the behavior and solutions of the problem. Additionally, a graph can also be used to make predictions and test different scenarios to find the most optimal solution to the problem.

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