which function shows a fabric with a price of $1.25 per square yard?

2 min read 15-01-2025

which function shows a fabric with a price of $1.25 per square yard?

Finding the right function to represent the cost of fabric priced at $1.25 per square yard is simpler than you might think. This article will explore how to represent this relationship mathematically, using different approaches and highlighting the key concepts involved.

Understanding the Problem

The core problem is to translate a real-world scenario – the cost of fabric – into a mathematical function. We know the price is constant: $1.25 per square yard. This means the total cost is directly proportional to the area of fabric purchased.

The Linear Function: The Simplest Solution

The most straightforward way to represent this is with a linear function. Linear functions are characterized by a constant rate of change. In this case, the rate of change is the price per square yard.

Let's define:

C: The total cost of the fabric (in dollars)
A: The area of the fabric (in square yards)

The function can then be expressed as:

C(A) = 1.25A

This function clearly shows that the total cost (C) is equal to 1.25 times the area (A). If you buy 2 square yards, the cost will be 1.25 * 2 = $2.50. If you buy 10 square yards, the cost will be 1.25 * 10 = $12.50.

Visualizing the Function

This linear relationship can easily be visualized as a graph. The graph would be a straight line passing through the origin (0,0) with a slope of 1.25. The slope represents the price per square yard.

[Insert a graph showing a linear function C(A) = 1.25A. X-axis should be A (area), Y-axis should be C (cost). The line should have a positive slope.]

Image Alt Text: Graph depicting the linear relationship between fabric area (square yards) and total cost (dollars) at a price of $1.25 per square yard.

Other Representations (Less Common but Valid)

While the linear function is the most efficient and intuitive representation, there are other ways to express this relationship, although they are less practical in this context:

Piecewise Function: While unnecessary here, you could technically use a piecewise function if, for example, there were different pricing tiers for bulk orders. However, with a consistent price per square yard, a simple linear function is sufficient.
Table of Values: A table showing different areas and their corresponding costs could be used, but this is not a mathematical function in itself; rather, it's a representation of the data generated by the function.

Choosing the Right Function

For a constant price per square yard, the linear function, C(A) = 1.25A, is the best and most concise way to represent the cost. It's straightforward, easily understandable, and accurately reflects the relationship between the area of fabric and its total cost. Using a more complex function would be unnecessarily complicated.

Conclusion

The function that accurately represents the cost of a fabric priced at $1.25 per square yard is a simple linear function: C(A) = 1.25A. This function directly and efficiently shows the relationship between the area of the fabric and its total cost, making it the ideal solution for this scenario. Understanding this fundamental relationship is crucial for anyone working with pricing and calculations related to fabric or similar materials.