In this second introductory lesson, students learn the term function for a rule that produces a single output for a given input. They also start to connect function language to language they learned in earlier grades about independent and dependent variables.
We can say, "the output is a function of the input," and we also say, "the output depends on the input." In the optional activity, students see how it is possible to use different words to describe the same function as long as all input-output pairs are the same. This helps solidify the notion of a function as something different from the method of calculating its values.
- Comprehend the structure of a function as having one and only one output for each allowable input.
- Describe (orally and in writing) a context using function language, e.g., “the [output] is a function of the [input]” or “the [output] depends on the [input]”.
- Identify (orally) rules that produce exactly one output for each allowable input and rules that do not.
Let’s learn what a function is.
- I know that a function is a rule with exactly one output for each allowable input.
- I know that if a rule has exactly one output for each allowable input, then the output depends on the input.
A function is a rule that assigns exactly one output to each possible input.
The function \(y=6x+4\) assigns one value of the output, \(y\), to each value of the input, \(x\). For example, when \(x\) is 5, then \(y=6(5)+4\) or 34.