Beginning Algebra Made Useful

Activity 5.

Before we begin, let's talk about the word, function. We used the word function a few times in Chapter 1 without defining it. For our purposes, function and equation are almost interchangeable. Equations are more general than functions. Here are some equations:

Some of the equations above are also functions. Can you guess which equations are also functions? Circle them. Why do you think these are functions and the others are not?

There are several mathematical definitions of function online. Here are two of them:

• A function is a special relationship where each input has a single output. (Math is Fun, online website¹⁴, retrieved April 16, 2020.)

• A technical definition of a function is: a relation¹⁵ from a set of inputs to a set of possible outputs where each input is related to exactly one output. (Math Insight, online website¹⁶, retrieved April 16, 2020.)

Let $x$ be the variable representing the set of input values. Let $y$ be the variable representing the set of output values. Use one of these definitions to determine which of the equations above are functions. Be ready to explain your choices.