Functions


 * Functions**

__Relation:__ A set of ordered pairs; values of the independent variable are paired with values of the dependent variable.

__Function:__ A relation in which each value of the independent variable corresponds to only one value of the dependent variable.

__Domain:__ The set of all the values of the independent variable of a relation. The input values.

__Range:__ The set of all the values of the dependent variable of a relation. The output values.

Method of representing a function:

1. Equation: f (x) = x + 1

2. Mapping Diagam

3. Ordered Pairs {(--3,1),(-1,5), (1,-2), (7,6)}

4.Table of Values value || y value ||
 * x
 * - 2 || -7 ||
 * 0 || 8 ||
 * 2 || 4 ||
 * 5 || -1 ||

5. Graph

__Activity:__ Find an example of a function.

1) Find an object that is an example of or can be represented by a function. 2) Describe, Sketch or take a picture of the object. 3) Explain why the object is a function. 4) If possible, represent your object using one of the methods described above. 5) Add your example to the wiki.

Example 1 - Rosh, Celton & Mbita 1. The ripple tank in the science arcade. . 2. Above. 3. The ripple tank represents a function as for every distance away from the center, the waves in the tank are only one height. 4. A sinusoidal graph representing this function, with the x axis corresponding to the distance away from the center piece, and y axis corresponding to the height of the wave.

Example 2 - Matthew, Alyssa, Cheryl 1. The human sponge apparatus in the Living Earth exhibit. 2. Step on the platform, and when you press start, a tube will fill up with water showing you how much water is in your body. 3. In this case, time is the independent variable and the volume of water in the tube is the dependent variable. Since time cannot go backwards, this relation is also a function. 4. This situation can be represented by a an absolute value function because the tube fills with water at a constant rate. When the desired volume is filled, it empties out at a constant rate. (see below)

Example 3 - Christa, Mark, Tristiana 1. A measurement of the sun's position in the sky at different times (forget specifically what exhibit) 2. It was a weather graph that showed several different factors that create weather such as amount of rain, sunshine per day, etc. We focused on one set of information which was the sun's position in the sky. The x-axis was the position in the sky and the y-axis was the date. 3. This is a function because it passes the vertical line test. Also, there is a dependant (date) and independent (position in the sky) variable. 4. This was the general shape of the graph (it was a sin/cos graph)

Example 4 - Natasha, George, Monette 1. Can you read the wave ? Mind Works Exhibit 2. 3. This is a function because it passes the vertical line test. Also, it is a sinusoidal function, continuing at a constant rate. Finally, there is a dependent(height) and independent (distance) variable. 4. This is an example of what this sinusoidal function looks like. The x-axis is the distance that is travelled, and the y-axis is the height of the waves.

Example 5 - Megan, Adam, Katie

The tornado simulation.

Height being the independent variable and width as the dependent variable this tornado represents a function because for every measure of height there is only one width.

Because we do not know the exact measurements or equation of the tornado we cannot represent the function with any of the methods described above.