Relations & Functions Unit 2, Lesson 1

What is a relation? In math, a relation is just a set of ordered pairs. {(1, 2), (-2, 3), (0, -3)} There is absolutely nothing special at all about the numbers that are in a relation.

What is a relation? A relation can also be represented by a table, a graph, or a mapping.

Example #1 Express the relation {(3, 2), (-1, 2), (0, -3), (-2, -2)} as a table, a graph, and a mapping. Mapping 2 -3 -2 3 -1

Domain & Range The set of the first numbers of the ordered pairs is the domain. The set of second numbers of the ordered pairs is the range.

Example #2 Determine the domain and range of the relation {(3, 2), (-1, 2), (0, -3), (-2, -2)}. Domain: {3, -1, 0, -2} Range: {2, -3, -2}

What is a function? A function is a special kind of relation. At first glance, a function looks just like a relation: It's a set of ordered pairs. It has a domain and a range made up of the x- and y-values of the ordered pairs. In mathematics, what distinguishes a function from a relation is that each x-value in a function has one and only ONE y-value. Some people find it helpful to think of the domain and range as people in romantic relationships. If each number in the domain is a person and each number in the range is a different person, then a function is when all of the people in the domain have 1 and only 1 boyfriend/girlfriend in the range.

Example #3 Determine whether each relation is a function: IS NOT IS IS B. C. {(-2, 4), (1, 5), (3, 6), (5, 8), (7, 10)} D. IS NOT IS IS IS

What is a function? The vertical line test is a way to determine whether or not a relation is a function. The vertical line test simply states that if a vertical line intersects the relation's graph in more than one place, then the relation is a NOT a function.

Example #4 Determine whether each relation is a function: IS NOT IS B. C. D. E. IS NOT IS IS NOT IS NOT IS

More Relations & Functions Unit 2, Lesson 2

Let’s review: relation domain range function A ________________ is any set of ordered pairs. The set of all first coordinates is called the ____________. The set of all second coordinates is called the __________. In a ________________, each element of the domain is assigned to one and only one element from the range. relation domain range function

Function or not a function? Each _____ has one and only one _____. (state, capital city) (date, person born on that date) (first name, last name) (city, area code) (student, school ID number) (person, birthdate) is a function not a function Give examples of not a function not a function is a function is a function

Independent & Dependent Variables The domain value for a relation is sometimes referred to as an input, and the resulting range value as an output. Formally, the domain value is called the independent variable and the range value is called the dependent variable (because it depends on the domain value).

Example #5 (2, 35) – on day 2, the average temperature was 35°F Name the ordered pair at point A and explain what it represents. Identify the independent and dependent variables for the relation. Is this relation a function? “Day” is the independent variable. “Temperature (°F)” is the dependent variable. YES – no “Day” is repeated

Continuous or Discrete? A continuous function can be graphed with a line or a smooth curve. A discrete function has a graph where the points are not connected.

Example #6 Classify each of the following situations as continuous or discrete: daily attendance at the zoo heart rate while exercising calories per serving photos per page in an album amount of iced tea remaining in a pitcher money earned for selling candy bars students per bus on a field trip number of pizzas sold over time discrete continuous continuous discrete continuous discrete discrete discrete

Domain: # of dogs walked Range: amount earned ($) Example #7 Is this function continuous or discrete? State the domain and range. discrete Domain: # of dogs walked D = {1, 2, 3, 4, 5, 6, 7, 8} Range: amount earned ($) R = {5, 10, 15, 20, 25, 30, 35, 40}

Range: sales ($ millions) Example #8 Is this function continuous or discrete? State the domain and range. continuous Domain: year D = {1999 - 2006} Range: sales ($ millions) R = {$0 - $5,000,000}