Graph: \[$ Y = 0.5|x| \$\]The Graph Of The Function \[$ F(x) = 0.5|x| \$\] Is \[$\square\$\] Than Its Parent Graph, \[$ F(x) = |x| \$\].$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -2.5 & 4 \\ & \\ &
Understanding the Graph of the Function f(x) = 0.5|x|
The graph of the function f(x) = 0.5|x| is a classic example of a function that exhibits symmetry and has a unique shape. In this article, we will delve into the properties of this function and explore its graph in detail.
What is the Parent Graph of f(x) = 0.5|x|?
The parent graph of f(x) = 0.5|x| is the graph of the function f(x) = |x|. This function is known as the absolute value function, and its graph is a V-shaped graph that opens upwards. The graph of f(x) = |x| has a minimum point at (0, 0) and has two arms that extend outwards from this point.
How Does the Graph of f(x) = 0.5|x| Differ from Its Parent Graph?
The graph of f(x) = 0.5|x| is similar to its parent graph, but it is stretched vertically. This means that the graph of f(x) = 0.5|x| is compressed horizontally compared to its parent graph. As a result, the graph of f(x) = 0.5|x| has a more steep slope than its parent graph.
Key Features of the Graph of f(x) = 0.5|x|
The graph of f(x) = 0.5|x| has several key features that are worth noting:
- Symmetry: The graph of f(x) = 0.5|x| is symmetric about the y-axis. This means that if we reflect the graph about the y-axis, we will get the same graph back.
- Minimum Point: The graph of f(x) = 0.5|x| has a minimum point at (0, 0). This point is the lowest point on the graph and is the vertex of the V-shaped graph.
- Arms: The graph of f(x) = 0.5|x| has two arms that extend outwards from the minimum point. These arms are steeper than the arms of the parent graph and are more steep.
- X-Intercepts: The graph of f(x) = 0.5|x| has two x-intercepts at (-2.5, 0) and (2.5, 0). These points are where the graph intersects the x-axis.
Graph of f(x) = 0.5|x|
The graph of f(x) = 0.5|x| is shown below:
| x | y |
|---|---|
| -2.5 | 4 |
| -2 | 3.5 |
| -1.5 | 3 |
| -1 | 2.5 |
| -0.5 | 2 |
| 0 | 1 |
| 0.5 | 2 |
| 1 | 2.5 |
| 1.5 | 3 |
| 2 | 3.5 |
| 2.5 | 4 |
Discussion
The graph of f(x) = 0.5|x| is a classic example of a function that exhibits symmetry and has a unique shape. The graph is similar to its parent graph, but it is stretched vertically, which means that it is compressed horizontally. The graph has several key features, including symmetry, a minimum point, arms, and x-intercepts. Understanding the graph of f(x) = 0.5|x| is important in mathematics and has many practical applications.
Conclusion
In conclusion, the graph of f(x) = 0.5|x| is a unique and interesting function that exhibits symmetry and has a V-shaped graph. The graph is similar to its parent graph, but it is stretched vertically, which means that it is compressed horizontally. Understanding the graph of f(x) = 0.5|x| is important in mathematics and has many practical applications.
References
- [1] "Graph of the Function f(x) = 0.5|x|". Math Open Reference. Retrieved 2023-02-26.
- [2] "Absolute Value Function". Math Is Fun. Retrieved 2023-02-26.
Further Reading
- [1] "Graph of the Function f(x) = |x|". Math Open Reference. Retrieved 2023-02-26.
- [2] "Properties of the Absolute Value Function". Math Is Fun. Retrieved 2023-02-26.
Graph: { y = 0.5|x| $}$ Q&A
Frequently Asked Questions about the Graph of f(x) = 0.5|x|
The graph of the function f(x) = 0.5|x| is a classic example of a function that exhibits symmetry and has a unique shape. In this article, we will answer some of the most frequently asked questions about the graph of f(x) = 0.5|x|.
Q: What is the parent graph of f(x) = 0.5|x|?
A: The parent graph of f(x) = 0.5|x| is the graph of the function f(x) = |x|. This function is known as the absolute value function, and its graph is a V-shaped graph that opens upwards.
Q: How does the graph of f(x) = 0.5|x| differ from its parent graph?
A: The graph of f(x) = 0.5|x| is similar to its parent graph, but it is stretched vertically. This means that the graph of f(x) = 0.5|x| is compressed horizontally compared to its parent graph.
Q: What are the key features of the graph of f(x) = 0.5|x|?
A: The graph of f(x) = 0.5|x| has several key features, including:
- Symmetry: The graph of f(x) = 0.5|x| is symmetric about the y-axis.
- Minimum Point: The graph of f(x) = 0.5|x| has a minimum point at (0, 0).
- Arms: The graph of f(x) = 0.5|x| has two arms that extend outwards from the minimum point.
- X-Intercepts: The graph of f(x) = 0.5|x| has two x-intercepts at (-2.5, 0) and (2.5, 0).
Q: What is the equation of the graph of f(x) = 0.5|x|?
A: The equation of the graph of f(x) = 0.5|x| is f(x) = 0.5|x|.
Q: How can I graph the function f(x) = 0.5|x|?
A: You can graph the function f(x) = 0.5|x| by using a graphing calculator or by plotting points on a coordinate plane.
Q: What are some real-world applications of the graph of f(x) = 0.5|x|?
A: The graph of f(x) = 0.5|x| has many real-world applications, including:
- Physics: The graph of f(x) = 0.5|x| can be used to model the motion of an object that is moving in a straight line.
- Engineering: The graph of f(x) = 0.5|x| can be used to model the behavior of a system that is subject to a constant force.
- Economics: The graph of f(x) = 0.5|x| can be used to model the behavior of a market that is subject to a constant demand.
Q: What are some common mistakes to avoid when graphing the function f(x) = 0.5|x|?
A: Some common mistakes to avoid when graphing the function f(x) = 0.5|x| include:
- Not using a graphing calculator: Not using a graphing calculator can make it difficult to accurately graph the function.
- Not plotting enough points: Not plotting enough points can make it difficult to accurately graph the function.
- Not using the correct equation: Not using the correct equation can result in an inaccurate graph.
Conclusion
In conclusion, the graph of f(x) = 0.5|x| is a unique and interesting function that exhibits symmetry and has a V-shaped graph. Understanding the graph of f(x) = 0.5|x| is important in mathematics and has many practical applications. By answering some of the most frequently asked questions about the graph of f(x) = 0.5|x|, we can gain a deeper understanding of this function and its many uses.
References
- [1] "Graph of the Function f(x) = 0.5|x|". Math Open Reference. Retrieved 2023-02-26.
- [2] "Absolute Value Function". Math Is Fun. Retrieved 2023-02-26.
Further Reading
- [1] "Graph of the Function f(x) = |x|". Math Open Reference. Retrieved 2023-02-26.
- [2] "Properties of the Absolute Value Function". Math Is Fun. Retrieved 2023-02-26.