Difference between revisions of "1.1 Functions"
Nwakefield2 (talk | contribs) |
Nwakefield2 (talk | contribs) |
||
| Line 33: | Line 33: | ||
}} | }} | ||
{{Ex-end}} | {{Ex-end}} | ||
| + | |||
| + | You'll now want to define what a function is. Start by using the terms '''input''' and '''output''' to describe bubbles in your bubble diagram. Say the definition twice for emphasis. | ||
| + | |||
| + | A '''function''' is a relation (or a rule) that assigns each input to only one output. | ||
| + | |||
| + | We are not introducing function notation just yet, that comes shortly. Stress the importance of using and understanding precise language. Tell your students that if they are ever asked if a relationship is a function, they have to show that the relation either fulfills or violates the definition of a function. | ||
Revision as of 23:46, 26 May 2020
Objectives:
- Determine when a relationship is a function and determine its inputs and outputs
- Represent relations/functions as tables, ordered pairs, graphs, equations, etc.
- Review graphs and the vertical line test
- Definitions
- function
Lesson Guide
Determine when a relationship is a function and determine its inputs and outputs
[15 minutes] Begin this lesson by giving examples of relationships between two sets. Examples should be easy to understand. I.e., use real world examples such as the days of the year and their average daily temperatures or the students in your class and the month they were born. Discuss how we can identify objects in the two sets and call this identification a “relation.”
A lot of this class will be about exploring the relationship between different pieces of information. For example:
|
Instructor Example |
Suggested Example |
|---|---|
|
This is a sentence that is in place to generate space in the table |
If we have a very special kind of relationship called a ``function," we can use one piece of information, called the input, to completely predict the other piece of information, called the output. It is often useful to take a few minutes and draw bubble diagrams of the examples you are going over. E.g.
|
You'll now want to define what a function is. Start by using the terms input and output to describe bubbles in your bubble diagram. Say the definition twice for emphasis.
A function is a relation (or a rule) that assigns each input to only one output.
We are not introducing function notation just yet, that comes shortly. Stress the importance of using and understanding precise language. Tell your students that if they are ever asked if a relationship is a function, they have to show that the relation either fulfills or violates the definition of a function.
