Given The Function Below, Fill In The Table Of Values And Use The Table Values To Graph.${ Y = -2 }$[ \begin{tabular}{|c|c|} \hline X X X & Y = − 2 Y = -2 Y = − 2 \ \hline -3 & -2 \ \hline -2 & -2 \ \hline -1 & -2 \ \hline 0 & -2 \ \hline 1 & -2
Introduction
In mathematics, functions are used to describe the relationship between two variables. A function is a set of rules that assigns to each input value, or independent variable, a unique output value, or dependent variable. In this article, we will explore a simple function and fill in a table of values based on the given function. We will also use the table values to graph the function.
The Function
The given function is:
This function states that for any value of x, the corresponding value of y is always -2. This means that the function is a horizontal line that intersects the y-axis at -2.
Filling in the Table of Values
To fill in the table of values, we need to substitute different values of x into the function and calculate the corresponding values of y. The table of values is shown below:
| x | y = -2 |
|---|---|
| -3 | -2 |
| -2 | -2 |
| -1 | -2 |
| 0 | -2 |
| 1 | -2 |
As we can see, the value of y is always -2 for any value of x. This is because the function is a horizontal line that intersects the y-axis at -2.
Graphing the Function
To graph the function, we can use the table of values to plot points on a coordinate plane. Since the value of y is always -2, we can plot points on the y-axis at -2. The graph of the function will be a horizontal line that intersects the y-axis at -2.
Discussion
The function y = -2 is a simple example of a linear function. Linear functions are functions that can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0, and the y-intercept is -2.
The graph of the function y = -2 is a horizontal line that intersects the y-axis at -2. This means that the function has no x-intercepts, since the value of y is always -2.
Conclusion
In conclusion, we have filled in the table of values for the function y = -2 and used the table values to graph the function. The graph of the function is a horizontal line that intersects the y-axis at -2. This is a simple example of a linear function, and it can be used to model real-world situations where the value of y is always constant.
Applications of the Function
The function y = -2 has several applications in real-world situations. For example, it can be used to model the height of a object that is always at a constant height, such as a building or a bridge. It can also be used to model the temperature of a object that is always at a constant temperature, such as a refrigerator or a freezer.
Real-World Examples
- Height of a Building: Suppose we want to model the height of a building that is always 100 feet tall. We can use the function y = -2 to model the height of the building, where y is the height and x is the number of floors.
- Temperature of a Refrigerator: Suppose we want to model the temperature of a refrigerator that is always 40°F. We can use the function y = -2 to model the temperature of the refrigerator, where y is the temperature and x is the number of hours.
Conclusion
Introduction
In our previous article, we explored the function y = -2 and filled in a table of values based on the given function. We also used the table values to graph the function. In this article, we will answer some frequently asked questions about the function y = -2.
Q: What is the value of y for any value of x?
A: The value of y is always -2 for any value of x. This is because the function is a horizontal line that intersects the y-axis at -2.
Q: Is the function y = -2 a linear function?
A: Yes, the function y = -2 is a linear function. Linear functions are functions that can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0, and the y-intercept is -2.
Q: What is the slope of the function y = -2?
A: The slope of the function y = -2 is 0. This means that the function is a horizontal line that does not change in value as x changes.
Q: What is the y-intercept of the function y = -2?
A: The y-intercept of the function y = -2 is -2. This means that the function intersects the y-axis at -2.
Q: Can the function y = -2 be used to model real-world situations?
A: Yes, the function y = -2 can be used to model real-world situations where the value of y is always constant. For example, it can be used to model the height of a object that is always at a constant height, such as a building or a bridge.
Q: What are some real-world examples of the function y = -2?
A: Some real-world examples of the function y = -2 include:
- The height of a building that is always 100 feet tall
- The temperature of a refrigerator that is always 40°F
- The amount of money in a bank account that is always $100
Q: Can the function y = -2 be used to model situations where the value of y changes over time?
A: No, the function y = -2 cannot be used to model situations where the value of y changes over time. This is because the function is a horizontal line that does not change in value as x changes.
Q: How can the function y = -2 be graphed?
A: The function y = -2 can be graphed by plotting points on a coordinate plane. Since the value of y is always -2, we can plot points on the y-axis at -2. The graph of the function will be a horizontal line that intersects the y-axis at -2.
Conclusion
In conclusion, the function y = -2 is a simple example of a linear function that can be used to model real-world situations where the value of y is always constant. It can be used to model the height of a object, the temperature of a object, and other real-world situations. We hope that this Q&A article has helped to clarify any questions you may have had about the function y = -2.