Let’s take a look at some key vocabulary needed as we begin Algebra 1  Function Vocabulary Let’s take a look at some key vocabulary needed as we begin Algebra 1. Label each of the blanks in the diagram below with the following: x-axis, y-axis, Quadrant I, Quadrant II, Quadrant III, Quadrant IV, origin, the coordinates of the origin and when x is positive or negative and when y is positive or negative in the ordered pair (+, +). y Quad I Quad II ( , ) ( , ) ( , ) ( , ) ( , ) + + - + x Origin 0 0 Quad IV Quad III + - - - The Cartesian Coordinate System is used to graph relationships between quantities. It is composed of two number lines called the x-axis and the y-axis. These two number lines divide the plane into four quadrants. A point or ordered pair is written as (x, y) or (x, f(x)) and can be located in any quadrant or on the x-axis or y-axis. NOTE: Another way to write y is f(x). Relations can be graphed as a point or a set of points. In which quadrant would each of the given points be located? (-2, 3) Quadrant II (0, 0) Origin, intersection of the x and y axes (2, -5) Quadrant IV (0, 4) Not in a quadrant but on the y-axis The domain of the relation is the set of permissible x-values. Domains can either be continuous or discrete Discrete data are individual points that would not be connected when graphed because not all x-values are included in the domain. The domain for discrete data is written using roster or set notation. Ex. Number of stamps and the cost. You cannot buy part of a stamp therefore you could not connect the points on the graph. D: {1,2,3,4} Continuous data are an infinite number of points that are connected when graphed because all x-values can be included in the domain. The domain for continuous data is written using an inequality. Ex. Number of hours worked and pay. You can work a portion of an hour and get paid for it so you could connect the points on the graph. D: 0 ≤ x ≤ 10 The Range of a relation is the set of permissible y-values. Relations in which each element of the domain is paired with exactly one element of the range are called functions. If the set of data is a function: one x value is paired with a unique y value x values don't repeat Vertical Line Test: vertical line only goes through one point Therefore, all functions are relations but all relations are not functions. Function Analogy: Think of domain as the set of people on a bus. The bus stops along the way are the range. The “function” of the bus is to deliver people to their stops. It is possible for 2 or more people to get off at one bus stop (y), however it is not possible for the same person (x) to get off at two different stops. Therefore, a person (x) is associated with only one bus stop (y). If the y-value increases as the x-value increases, the function is increasing. On the graph, the function will go up from left to right. If the y-value decreases as the x-values increases, the function is decreasing. On the graph, the function will go down from left to right. Think about our data collections Miles and Intersections and Burning Calories. Which ones were relations? Why? Both Miles and Intersections and Burning Calories are relations because both sets of data can be written as ordered pairs. Which ones were functions? Why? Burning Calories is a function since the x values cannot repeat. Was Burning Calories continuous or discrete? Why? Burning Calories is continuous because you can burn half a calorie in half a minute. You can take a fraction of the calories. What is the domain and range for Burning Calories? We need to think about all of the possible scenarios. D: {x ≥ 0} R: {y ≥ 0} Is the relationship in Burning Calories increasing or decreasing? Why? Burning Calories is increasing because the more calories you burn, the more time it takes.