Algebra:Functions
Tell whether each represents a function. Explain.
Area=LenghtxWidth
To determine whether the equation "Area = Length x Width" represents a function, we need to understand what a function is.
In mathematics, a function is a relation between two sets, where each input from the first set (called the domain) corresponds to only one output in the second set (called the range). In other words, for a given input, there should be a unique output, and no input should have multiple outputs.
In the equation "Area = Length x Width," the area is determined by multiplying the length and width. Let's consider an example to demonstrate whether this equation represents a function:
Suppose we have two rectangles with different lengths and widths: Rectangle A has a length of 4 units and a width of 5 units, while Rectangle B has a length of 2 units and a width of 10 units.
For Rectangle A, the area calculated using the equation is:
Area = Length x Width
Area = 4 x 5
Area = 20 square units
For Rectangle B, the area calculated using the equation is:
Area = Length x Width
Area = 2 x 10
Area = 20 square units
In this example, we can see that both Rectangle A and Rectangle B have an area of 20 square units, even though their lengths and widths are different. This implies that for a particular area value (in this case, 20 square units), there are multiple combinations of length and width that can produce that same area.
Therefore, the equation "Area = Length x Width" does not represent a function because it violates the definition of a function by having multiple inputs (length and width) with the same output (area).