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Exercises Functions

Example 1 from Algebra and Trigonometry, 3.1 Functions and Function Notation

Determining If Menu Price Lists Are Functions

The coffee shop menu, shown below, consists of items and their prices.
ⓐ Is price a function of the item?
ⓑ Is the item a function of the price?

A menu of donut prices from a coffee shop where a plain donut is $1.49 and a jelly donut and chocolate donut are $1.99.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
ⓐ Let’s begin by considering the input as the items on the menu. The output values are then the prices.

Each item on the menu has only one price, so the price is a function of the item.
ⓑ Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it. See the image below.

Therefore, the item is a not a function of price.

How did it go?

Next Determining If Class Grade Rules Are Functions

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.