Graphs 3.2

SAT Question: If, which of the following could be the values of a and b? A.a = -5, b = 0 B.a = -3, b = -4 C.a = 0, b = -1 D.a = ¾; b = 1 E.a = 1, b = -2 Yes!

Most of the relations we work with come from the Cartesian product R×R, where R is the set of Real Numbers. How many ordered pairs are in that set? infinite It’s very difficult to list them, so we use a _________ to show them. graph

Cartesian Coordinate System Axes y-axis x-axis ordered pair (x,y) origin

IIIIII IV Four Quadrants

Graph this relation on the following graph:

(x, y) Yes or No (-1,-4) -4 = 3(-1)-1 -4 = -4 yes (7, 5) Determine whether an ordered pair is a solution of an equation: Check for (-1,-4) and (7, 5). No

Graphing a relation There are several methods of graphing relations: 1.Plotting Points 2.Using the x and y intercepts. 3.Using a point (usually the y-intercept) and a slope. 4.Graphing horizontal and vertical lines.

x (x, y) -2 y = 3(-2) – 1 = -7 (-2,-7) y = 3(-1) – 1 = Today we’re going to use Plotting Points. Example: Graph (-1, -4) (0, -1) (1, 2) (2, 5) xy

xy Now put the ordered pairs on the graph and connect them:

If a relation has the form then it looks like the following graph. In order to make sure you get the entire picture of the graph, you need to make sure you choose enough ordered pairs. Graph xy

Classwork: 2, 16, 23, 31/114

(x, y)? Yes

xy

xy

Get ready for a “Small Quiz” to be written on your grade sheet.

The End

Quiz. Copy the problems and write the answer. Put your grade paper on the front of your row, quiz side down. 1.Is this a function? 2. 3.Find the domain of Write it in set-builder notation.