Functions!

Vocab Function Domain Range Relation

Definitions Function- a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable WHAT? There is only one y value for each x value

Def’n Continued Domain- Set of all possible values of the first variable – The x variable – The independent variable Range- Set of all possible values of the second variable – The y variable – The dependent variable

WHOA…Wait a minute So many words! Lets review a minute Variable- A factor that can be changed – May be in an experiment in science – May be a letter in math Independent Variable- The input of a function Dependent Variable-The output of a function, what changes when the independent variable changes

Functions Two main ways to represent functions Graphically, or through a table Remember, a function has only one y value for each x value Lets look at some examples

Is it a function? Domain, xRange, y Domain, xRange, y

Graphically VERTICAL LINE TEST If every very line intersects a given graph at no more than one point, then the graph represents a function

Is it a function?

Group member 1… Turn to group members 2 and 3 and give them another example of a graphic function

Domain and Range Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work. Most often a function's domain is all real numbers.

Consider a simple linear equation like the graph shown below. What values are valid inputs? Every number! It's range is all real numbers because there is nothing that won't work. The graph extends forever in the x directions.

What kind of functions don't have a domain of all real numbers? The kinds of functions that aren't valid for particular input values. Here is an example: What is the value of y when x=1? Well, it's 3 divided by 0, which is undefined. Therefore 1 is not in the domain of this function. All other real numbers are valid, so the domain is all real numbers except for x=1.

Domain Tricks The most common reason for limited domains is probably the divide by zero issue. When finding the domain of a function, first look for any values that cause you to divide by zero.

The range of a simple linear function is almost always going to be all real numbers. A graph of a line, such as the one shown below on the left, will extend forever in either y direction.

The exception: y=constant. When you have a function where y equals a constant (like y=3), your graph is a horizontal line. In that case, the range is just that one value. Otherwise, the range is usually real numbers.

To summarize: The domain of a function is all the possible input values, and the range is all possible output values.

Representing Domain and Range List the possible values of domain and range using set notation. Example: State the domain and range of the following relation. Is the relation a function? {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} Domain: {2,4,3,6} Range: {-3,6,-1,3} They do not have to be listed in order, and only need be listed once. Not a function because x values repeat

Try it in your groups State the domain and range of the following relation. Is the relation a function? {(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

Drop Bounce Lab Group Work

Follow directions in the lab Record your data in the table Lets discuss – Independent Variable – Dependent Variable – System of Measurement When you have finished, put your data on large sheet of paper and put on white board

Drop Bounce Data

Graphical Representation

Questions to Ponder Is the graph a function? What are two ways you can verify this? What is the domain? What is the range?

Domain and Range Graphically Hopefully these next few slides will help us make connections between points on a graph and the domain and range

Use the graph to find the domain and range of f(x) = sqrt(x).

Find the domain and range of f(x) = 1/x.

Find the domain and range

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