Introduction
Chapter Name : Relations And Functions |
Sub Topic Code : 104_11_02_01_01 |
Topic Name : Introduction |
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Sub Topic Name : Introduction |
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Introduction
Relation is property that connects two or more identities. Every relation has a pattern or property.Also, every relation involves minimum two identities. Function is a rule that connects two things. It is a set of actions or activities. A function can thus be represented in general as f(x)->y.
Pre-Requisites:
• Graphs • Polynomials • Sets • Operation on Sets
Activity:
Students can measure the diameter and circumference of several round containers or lids and record that data in a table. If diameter is the input and circumference is the output, what's the function rule? As they divide each container's circumference by its diameter to find that rule, they should notice a constant ratio -- a rough approximation of pi.
Real Life Question:
What are the different relations in a family?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Relation | Relation is property that connects two or more identities. |
| Function | Function is a rule that connects two things. It is a set of actions or activities. |
| Domain | The domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. |
| Range | The range of a function refers to either the co-domain or the image of the function, depending upon usage. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Ruler | Use a ruler to find the diameter of a circular container. |
| Thread | Use a thread to wrap round a circular container. Then measure the thread required by straightening it out on the ruler. |
Real life uses :
Some thermometers come with both Celsius and Fahrenheit scales. Students can study a thermometer as an input/output table. Students might be able to compare the two scales (noting, for instance, that 0° C = 32° F and 32° C = 50° F) and figure out the function rule -- the formula for converting from one scale to the other.
Places to visit :
Visit the Automatic Soda Machine in your school or in a Mall. The user puts in money, punches a specific button, and the soda can drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)
Practical examples around us
| Examples | Explainations |
|---|---|
| Shadows | The length of a shadow is a function of its height and the time of day. Shadows can be used to find the height of large objects such as trees or buildings. |
What you learn in Theory:
Definition of a Relation and a Function and their use.
What you learn in Practice:
To measure circumference of a container, calculate height of a tree using its shadow, derive function rule for scale change in a thermometer.