Fill In The Table Using This Function Rule:$\[ Y = -6x + 1 \\]
Introduction
In mathematics, a function rule is a mathematical equation that describes the relationship between two variables, typically denoted as x and y. The function rule is used to determine the output value (y) for a given input value (x). In this article, we will explore how to fill in a table using a given function rule, specifically the equation y = -6x + 1.
Understanding the Function Rule
The function rule y = -6x + 1 is a linear equation, which means that the graph of the equation is a straight line. The equation is in the slope-intercept form, where the slope (m) is -6 and the y-intercept (b) is 1.
- Slope (m): The slope of the line is -6, which means that for every unit increase in x, the value of y decreases by 6 units.
- Y-intercept (b): The y-intercept is 1, which means that the line intersects the y-axis at the point (0, 1).
Filling in the Table
To fill in the table using the function rule y = -6x + 1, we need to substitute different values of x into the equation and calculate the corresponding values of y.
| x | y = -6x + 1 |
|---|---|
| -2 | ? |
| -1 | ? |
| 0 | ? |
| 1 | ? |
| 2 | ? |
Step 1: Substitute x = -2 into the equation
y = -6(-2) + 1 y = 12 + 1 y = 13
| x | y = -6x + 1 |
|---|---|
| -2 | 13 |
| -1 | ? |
| 0 | ? |
| 1 | ? |
| 2 | ? |
Step 2: Substitute x = -1 into the equation
y = -6(-1) + 1 y = 6 + 1 y = 7
| x | y = -6x + 1 |
|---|---|
| -2 | 13 |
| -1 | 7 |
| 0 | ? |
| 1 | ? |
| 2 | ? |
Step 3: Substitute x = 0 into the equation
y = -6(0) + 1 y = 0 + 1 y = 1
| x | y = -6x + 1 |
|---|---|
| -2 | 13 |
| -1 | 7 |
| 0 | 1 |
| 1 | ? |
| 2 | ? |
Step 4: Substitute x = 1 into the equation
y = -6(1) + 1 y = -6 + 1 y = -5
| x | y = -6x + 1 |
|---|---|
| -2 | 13 |
| -1 | 7 |
| 0 | 1 |
| 1 | -5 |
| 2 | ? |
Step 5: Substitute x = 2 into the equation
y = -6(2) + 1 y = -12 + 1 y = -11
| x | y = -6x + 1 |
|---|---|
| -2 | 13 |
| -1 | 7 |
| 0 | 1 |
| 1 | -5 |
| 2 | -11 |
Conclusion
In this article, we have learned how to fill in a table using the function rule y = -6x + 1. We have substituted different values of x into the equation and calculated the corresponding values of y. The resulting table shows the relationship between the input values (x) and the output values (y) for the given function rule.
Tips and Variations
- Using different function rules: The same process can be applied to different function rules, such as y = 2x + 3 or y = x^2 + 1.
- Graphing the function: The function rule y = -6x + 1 can be graphed using a graphing calculator or software to visualize the relationship between x and y.
- Real-world applications: The function rule y = -6x + 1 can be used to model real-world situations, such as the cost of a product based on the number of units sold.
Q: What is a function rule?
A: A function rule is a mathematical equation that describes the relationship between two variables, typically denoted as x and y. The function rule is used to determine the output value (y) for a given input value (x).
Q: What is the purpose of filling in a table using a function rule?
A: The purpose of filling in a table using a function rule is to visualize the relationship between the input values (x) and the output values (y) for a given function rule. This can help to identify patterns and trends in the data.
Q: How do I fill in a table using a function rule?
A: To fill in a table using a function rule, you need to substitute different values of x into the equation and calculate the corresponding values of y. You can use a calculator or software to simplify the calculations.
Q: What if I have a function rule with a variable in the exponent?
A: If you have a function rule with a variable in the exponent, such as y = x^2 + 1, you can use the same process as before to fill in the table. However, you may need to use a calculator or software to simplify the calculations.
Q: Can I use a function rule to model real-world situations?
A: Yes, you can use a function rule to model real-world situations, such as the cost of a product based on the number of units sold. The function rule can be used to predict the output value (y) for a given input value (x).
Q: How do I determine the domain and range of a function rule?
A: To determine the domain and range of a function rule, you need to identify the values of x and y that are possible for the function. The domain is the set of all possible input values (x), and the range is the set of all possible output values (y).
Q: What is the difference between a function rule and an equation?
A: A function rule is a mathematical equation that describes the relationship between two variables, typically denoted as x and y. An equation is a statement that two expressions are equal. A function rule is a specific type of equation that describes a function.
Q: Can I use a function rule to solve a system of equations?
A: Yes, you can use a function rule to solve a system of equations. By substituting the function rule into one of the equations, you can solve for the unknown variable.
Q: How do I graph a function rule?
A: To graph a function rule, you can use a graphing calculator or software. You can also use a table of values to plot the points on a coordinate plane.
Q: What are some common function rules?
A: Some common function rules include:
- y = 2x + 3
- y = x^2 + 1
- y = -6x + 1
- y = x^3 - 2x^2 + x + 1
These are just a few examples of function rules. There are many other types of function rules that can be used to model real-world situations.
Conclusion
In this article, we have answered some frequently asked questions about filling in tables using function rules. We have discussed the purpose of filling in a table, how to fill in a table, and how to determine the domain and range of a function rule. We have also discussed some common function rules and how to graph a function rule. By following these tips and techniques, you can use function rules to model real-world situations and solve problems in mathematics.