1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
In our super-cyber information age, virtually everyone can work a computer. We have preteens learning code, preschoolers using iPads, and even grandma has branched out from solitaire to Facebook and Twitter ("@PriceIsRight just isn't the same without Bob Barker #disappointment").
In fact, many of your students are probably familiar with the computer science acronym GIGO. It stands for, "Garbage In, Garbage Out," meaning that a computer will do exactly what you tell it to do—not what you want it to do. If you put garbage in, you'll get garbage out.
In math, there are equations called functions that act a lot like computers. A function is a mathematical rule that assigns exactly one y value (the "output") to each x value (the "input"). The thing to remember about functions is that each x can have one and only one y. Though, interestingly enough, each y can have lots of x values, if you want.
Students should understand the concept of functions as having one output for every input. They should also be able to find the output value for a particular x value by plugging the number into the function wherever it has an x. It's also important that they know that the graph of a function represents all the ordered pairs (the different inputs-output combinations) that satisfy the function rule.
Warn your students not to try inputs and outputs of garbage. Those won't satisfy anything.
- Evaluate a Defined Operator Numerically - Math Shack
- Solving Equations Given One Variable - Math Shack
- What is a Function? - Math Shack
- Identifying Sets, Relations, and Functions - Math Shack
- Using Graphs to Determine Whether a Relation Is a Function - Math Shack
- Creating Tables for Linear Functions - Math Shack
- Solving More Complicated Equations - Math Shack