Chapter 1.7, Problem 58PPE

To determine

To find:

If the price paid is a function of the number of shirts purchased.

Answer to Problem 58PPE

The price paid is not a function of the number of shirts purchased because there are different total costs (35 and 36) for the same number of shirts i.e. 5 shirts. Or, option C is correct option.

Explanation of Solution

Given information:

Below table represents the price paid p for the number of shirts purchased n for the six stores:

  

Concept used:

While forming an ordered pair, independent variable is put as first number and dependent variable is put as second number. Further, a relation is a function if for each different first value, there is always a unique second value in its given ordered pairs. Or, if two first elements are same, then their associated second values should also be same.

Calculation:

Each column`s entries will represents a single ordered pair in form $(p,n)$ are $\left(5,35),\left(3,24\right),\left(5,36\right),\left(3,21\right),\left(4,28\right),(6,40\right)$ . In these ordered pairs, two pairs $(5,35)$ and $(5,36)$

are two pairs, having same first two values, but their second associated values are different, that are against the definition of the function.

Conclusion:

So, clearly the given relation in tabular form is not a function because there are two different total costs for the same number of shirts i.e. 5 shirts.