Complete The Remainder Of The Table For The Given Function Rule: Y = 4 − 3 X 4 Y = 4 - \frac{3x}{4} Y = 4 − 4 3 X ​ $[ \begin{tabular}{c|ccccc} x & -4 & 0 & 4 & 8 & 12 \ \hline y & 7 & 4 & {?} & {?} & {?}

Introduction

In mathematics, a function rule is a mathematical expression that describes the relationship between the input and output of a function. Given a function rule, we can use it to find the output value for a specific input value. In this article, we will focus on completing the remainder of the table for the given function rule: $y = 4 - \frac{3x}{4}$.

Understanding the Function Rule

The given function rule is $y = 4 - \frac{3x}{4}$. This means that for every input value of $x$, we can find the corresponding output value of $y$ by plugging in the value of $x$ into the function rule.

Completing the Table

To complete the remainder of the table, we need to find the output values of $y$ for the input values of $x$ that are not given in the table. We can do this by plugging in the values of $x$ into the function rule.

Finding the Output Value for x = 4

To find the output value for $x = 4$, we can plug in the value of $x$ into the function rule:

$$y = 4 - \frac{3(4)}{4}$$

Simplifying the expression, we get:

$$y = 4 - 3$$

$$y = 1$$

So, the output value for $x = 4$ is $y = 1$.

Finding the Output Value for x = 8

To find the output value for $x = 8$, we can plug in the value of $x$ into the function rule:

$$y = 4 - \frac{3(8)}{4}$$

Simplifying the expression, we get:

$$y = 4 - 6$$

$$y = -2$$

So, the output value for $x = 8$ is $y = -2$.

Finding the Output Value for x = 12

To find the output value for $x = 12$, we can plug in the value of $x$ into the function rule:

$$y = 4 - \frac{3(12)}{4}$$

Simplifying the expression, we get:

$$y = 4 - 9$$

$$y = -5$$

So, the output value for $x = 12$ is $y = -5$.

Conclusion

In this article, we have completed the remainder of the table for the given function rule: $y = 4 - \frac{3x}{4}$. We have found the output values of $y$ for the input values of $x$ that were not given in the table. The completed table is shown below:

x	y
-4	7
0	4
4	1
8	-2
12	-5

Discussion

The function rule $y = 4 - \frac{3x}{4}$ is a linear function, which means that it has a constant rate of change. The rate of change of the function is -3/4, which means that for every unit increase in $x$, the value of $y$ decreases by 3/4 units.

Mathematical Concepts

The mathematical concepts used in this article include:

• Function rules
• Linear functions
• Rate of change
• Input and output values

Real-World Applications

The function rule $y = 4 - \frac{3x}{4}$ has many real-world applications, such as:

• Modeling the cost of a product based on the number of units produced
• Calculating the distance traveled by an object based on its speed and time
• Determining the amount of money earned by an employee based on their hourly wage and number of hours worked

Conclusion

$$$$$$$$

Introduction

In our previous article, we completed the remainder of the table for the given function rule: $y = 4 - \frac{3x}{4}$. In this article, we will answer some frequently asked questions (FAQs) related to the function rule and completing the table.

Q: What is the purpose of completing the table for the given function rule?

A: The purpose of completing the table for the given function rule is to find the output values of $y$ for the input values of $x$ that are not given in the table. This helps us to understand the behavior of the function and make predictions about the output values for different input values.

Q: How do I know if the function rule is linear or non-linear?

A: To determine if the function rule is linear or non-linear, we need to check if the function rule can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. If the function rule can be written in this form, then it is a linear function. If not, then it is a non-linear function.

Q: What is the rate of change of the function rule?

A: The rate of change of the function rule is the slope of the function, which is -3/4 in this case. This means that for every unit increase in $x$, the value of $y$ decreases by 3/4 units.

Q: How do I find the output value of $y$ for a given input value of $x$?

A: To find the output value of $y$ for a given input value of $x$, we need to plug in the value of $x$ into the function rule and simplify the expression.

Q: What are some real-world applications of the function rule?

A: The function rule $y = 4 - \frac{3x}{4}$ has many real-world applications, such as:

• Modeling the cost of a product based on the number of units produced
• Calculating the distance traveled by an object based on its speed and time
• Determining the amount of money earned by an employee based on their hourly wage and number of hours worked

Q: How do I know if the function rule is a good model for a real-world situation?

A: To determine if the function rule is a good model for a real-world situation, we need to check if the function rule accurately predicts the output values for different input values. We can do this by comparing the predicted output values with the actual output values.

Q: What are some common mistakes to avoid when completing the table for the given function rule?

A: Some common mistakes to avoid when completing the table for the given function rule include:

• Not plugging in the values of $x$ into the function rule correctly
• Not simplifying the expression correctly
• Not checking if the function rule is linear or non-linear
• Not using the correct rate of change

Conclusion

In conclusion, completing the remainder of the table for the given function rule $y = 4 - \frac{3x}{4}$ requires understanding the function rule and plugging in the values of $x$ into the function rule. The function rule has many real-world applications and is an important concept in mathematics. By following the steps outlined in this article, you can complete the table for the given function rule and make predictions about the output values for different input values.

Additional Resources

For more information on completing the table for the given function rule, please refer to the following resources:

• Mathematics textbook
• Online math resources
• Math tutoring services

Final Thoughts

Completing the remainder of the table for the given function rule $y = 4 - \frac{3x}{4}$ is an important concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can complete the table for the given function rule and make predictions about the output values for different input values. Remember to always check if the function rule is linear or non-linear and to use the correct rate of change.