Lesson 1-8 Graphs and Functions

Definitions Functions- a relationship between input and output. Coordinate system- formed by the intersection of two lines, the horizontal axis and the vertical axis, a coordinate system can be used to graph a function.

Definitions ox y The vertical axis is also called the y-axis. The horizontal axis is also called the x-axis. The origin at (0,0) is the point where the axes intersect. (6,5) Each point is named by an ordered pair. The coordinate system is also called the coordinate plane.

Definitions Ordered pair - a set of numbers, or coordinates, written in the form (x, y). x-coordinate - the x value, corresponds with the x-axis. y-coordinate - the y value, corresponds with the y axis.

Example Refer to the graph on page 43 of the Student Edition. Name the ordered pair at point E and explain what it represents.

Dependent variable - the variable in the relation whose value depends on the value of the independent variable. (Graphed on the vertical axis) Independent variable - The variable in a function whose value is subject to choice. (Graphed on the horizontal axis) Definitions

Example In warm climates, the average amount of electricity used in homes each month rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and dependent variables in this function of temperature and electricity usage.

Relation - a set of ordered pairs. (1,5), (4, 6), ( 3, 3) Domain - the set of first numbers of the ordered pairs. {1, 3, 4} Range - the set of second numbers of the ordered pairs. {3, 5, 6} Definitions

Example There are three lunch periods at a school cafeteria. During the first period, 352 students eat lunch. During the second period, 304 students eat lunch. During the third period, 391 students eat lunch. 1.Make a table showing the number of students for each of the three lunch periods. 2.Write the data as a set of ordered pairs. 3.Draw a graph that shows the relationship between the lunch period and the number of students.

Example Mr. Mar is taking his biology classes to the zoo. The admission price is $4 per student, and at most, 120 students will go. Identify a reasonable domain and range for this situation. 1.Draw a graph that shows the relationship between the number of students who go to the zoo, and the total price of admission.