For The Function Defined By F ( X ) = X 2 X 2 F(x)=\frac{x^2}{x^2} F ( X ) = X 2 X 2 ​ , What Is The Constant Of Proportionality?A. 120 B. Undefined C. 12 D. 1200 Please Select The Best Answer From The Choices Provided: A B C D

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Introduction

In mathematics, a constant of proportionality is a value that represents the ratio of two quantities that are directly proportional to each other. In other words, it is a value that describes the relationship between two variables that change in a predictable and consistent manner. In this article, we will explore the concept of constant of proportionality and how it applies to the function defined by f(x)=x2x2f(x)=\frac{x^2}{x^2}.

What is Direct Proportionality?

Direct proportionality is a relationship between two variables where one variable increases or decreases in a predictable and consistent manner as the other variable changes. This relationship can be represented mathematically as y=kxy = kx, where yy is the dependent variable, xx is the independent variable, and kk is the constant of proportionality.

The Function Defined by f(x)=x2x2f(x)=\frac{x^2}{x^2}

The function defined by f(x)=x2x2f(x)=\frac{x^2}{x^2} is a simple rational function that can be simplified to f(x)=1f(x)=1. This function represents a constant value that does not change with respect to the input variable xx.

Finding the Constant of Proportionality

To find the constant of proportionality, we need to identify the ratio of the two quantities that are directly proportional to each other. In this case, the function f(x)=x2x2f(x)=\frac{x^2}{x^2} represents a constant value of 1, which means that the ratio of the two quantities is always 1.

Analyzing the Options

Now that we have found the constant of proportionality, let's analyze the options provided:

  • A. 120: This option is incorrect because the constant of proportionality is not 120.
  • B. Undefined: This option is incorrect because the constant of proportionality is not undefined.
  • C. 12: This option is incorrect because the constant of proportionality is not 12.
  • D. 1200: This option is incorrect because the constant of proportionality is not 1200.

Conclusion

In conclusion, the constant of proportionality for the function defined by f(x)=x2x2f(x)=\frac{x^2}{x^2} is 1. This is because the function represents a constant value that does not change with respect to the input variable xx. Therefore, the correct answer is not among the options provided.

Final Answer

Introduction

In our previous article, we explored the concept of constant of proportionality and how it applies to the function defined by f(x)=x2x2f(x)=\frac{x^2}{x^2}. In this article, we will answer some frequently asked questions about constant of proportionality to help you better understand this concept.

Q: What is the difference between direct proportionality and inverse proportionality?

A: Direct proportionality is a relationship between two variables where one variable increases or decreases in a predictable and consistent manner as the other variable changes. Inverse proportionality, on the other hand, is a relationship between two variables where one variable decreases as the other variable increases, and vice versa.

Q: How do I identify the constant of proportionality in a given function?

A: To identify the constant of proportionality, you need to look for the ratio of the two quantities that are directly proportional to each other. In a function, this ratio is often represented by a constant value that does not change with respect to the input variable.

Q: Can the constant of proportionality be a variable?

A: No, the constant of proportionality cannot be a variable. By definition, a constant of proportionality is a value that represents the ratio of two quantities that are directly proportional to each other. If the constant of proportionality is a variable, then it is not a constant of proportionality.

Q: How do I apply the concept of constant of proportionality in real-life situations?

A: The concept of constant of proportionality is widely used in various fields, including physics, engineering, economics, and finance. For example, in physics, the constant of proportionality is used to describe the relationship between the force applied to an object and the resulting acceleration. In economics, the constant of proportionality is used to describe the relationship between the price of a good and the quantity demanded.

Q: Can the constant of proportionality be negative?

A: Yes, the constant of proportionality can be negative. In fact, many real-world relationships involve negative constants of proportionality. For example, in the relationship between the force applied to an object and the resulting acceleration, the constant of proportionality is often negative.

Q: How do I graph a function with a constant of proportionality?

A: To graph a function with a constant of proportionality, you need to plot the input variable on the x-axis and the output variable on the y-axis. The graph will be a straight line with a slope equal to the constant of proportionality.

Q: Can the constant of proportionality be zero?

A: No, the constant of proportionality cannot be zero. If the constant of proportionality is zero, then the two quantities are not directly proportional to each other.

Conclusion

In conclusion, the concept of constant of proportionality is a fundamental idea in mathematics that describes the relationship between two quantities that are directly proportional to each other. By understanding this concept, you can apply it to various real-life situations and solve problems in physics, engineering, economics, and finance.

Final Answer

The final answer is that the constant of proportionality is a value that represents the ratio of two quantities that are directly proportional to each other. It is a fundamental concept in mathematics that has many real-world applications.