Introduction+to+Functions+(Graph,+Slope,+and+Equations)

= This website was created by Tim Kickham and was updated: 12/4/08 = =Definitions= Let's say we have an ordered pair like {(1,-1),(1,1),(4,4),(4,-4),(0,0)}. The ordered pair is called a **relation.** The first term in each pair of ordered pairs is called a **domain**. The domain in this example is {1,4,0}. The second set of terms is known as the **range.** The range for this example is {-1,1,4,-4,0}. If there are no repeating numbers in the ordered pairs then the relation is called a **function**. The most common way to define a function is with what is called a **formula**. A formula relates an element in the domain with a unique element in the range. An example of a function is f(x) = 2x. This is read "f of x equals 2 times x." The **composition** of functions is applying one function after another function. See example 2.

=Examples= For example: //f//(//x//) = 3//x// - 5. If //x// equals 8 solve the function. To do this, plug 8 into all //x// variables and solve. //f//(8) = 3 times 8 minus 5 which equals 19. //f//(//g//(//x//))(3) = //f//(//g//(3) = //f//(3^2) = //f//(9) + 1 = 19 //g//(//f//(//x//))(3) = //g//(//f//(3)) = //g//(2(3) + 1) = //g//(7) = 7^2 = 49. Since 19 doesn't equal 49 the functions are not commutative. //f//(//x//) = __x - 1__ 2 (//f//(9) = __9 - 1__ 2 (//f//(9) = __8__ 2 (//f//(9) = 4
 * 1**.To solve a function you plug in the value given into the variable in parenthesis.
 * 2**. If //f//(//x//) = 2//x//+1 and //g//(//x//) = //x//^2, determine the value of //f//(//g//(//x//)) and //g//(//f//(//x//)) if //f//(//g//) and //g//(//f//) equals 3.
 * 3**. If //f(x)// equals 9 solve the function:

=Quiz Questions= 1. What is an ordered pair known as?

2. What way is used most often to define a function?

3. What's an example of a composition of a function?

4.If x equals 3 solve the following function: //f//(//x//) = 10x-9

5. If x equals 10 solve the following function: f(x) = x/2 + 8

=YouTube Video= This video is an introduction to functions: media type="youtube" key="Uw8crn39reA" height="344" width="425" Video Citation: Functions - An Introduction. 2007.Video. http://www.youtube.com/watch?v=Uw8crn39reA =Quiz Answers= 1. An ordered pair is known as a function. 2. The most common way to define a function is using a formula. 3. An example of a composite function would be: //f//(//x//(//l//). 4.10 times 3 = 30 minus 9 = 21. 5. 10 divided by 2 = 5 plus 8 = 13. =Additional Links:= The website above will further explain what a relation, function, domain and range is. It will teach you to find the domain and range of a relation. It will tell you how to identify whether a relation is a function or not. It will explain what the vertical line test is and how to evaluate functional values. This website will provide extra explanations and it even has math problems at the bottom of the webpage.
 * 1**. [|**http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut13_func.htm**]
 * 2**.http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_FunctionsRelationsIntro.xml