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Is the relation between the side length and the area of a square a function? Explain

User Neleus
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Answer:

Yes

Explanation:

Relationships can be defined as a function if all x-values are unique.

Area of a Square

First, let's find a relationship that can describe the area of a square. We know that the area of squares and rectangles is A = l*w, where A is the area, l is the length, and w is the width. However, in a square, length and width are equal. So, we can replace the l with another w. This creates the equation A = w*w, which is A = w². This is an acceptable answer, but functions are usually given in terms of y and x. So, let's replace A with y and w with x.

  • y = x²

In this equation, y is the area and x is the width.

Functions

Now, we need to determine if y = x² is a function. We can say that an equation is a function when every x-value only gives 1 y-value. For example, if we plug 2 in for x, we only get y = 4. There are no other y-values when x = 2. This statement is true for all x-values Thus, the relation between the sides and area of a square, y = x², is a function.

Additionally, if the equation is graphed, we can tell that there is no x-value that has 2 corresponding y-values. Every x-value has exactly 1 corresponding y-value. Therefore, the equation is a function.

Is the relation between the side length and the area of a square a function? Explain-example-1
User Rob L
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