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1.7 Represent Functions as Graphs Goal Represent functions as graphs. GRAPHING A FUNCTION You can use a graph to represent a _______________. In a given table, each corresponding pair of input and output values forms an______________. An ordered pair of numbers can be plotted as a _____________. The x -coordinate is the ____________. The y -coordinate is the _____________. The horizontal axis of the graph is labeled with the ___________________. The vertical axis is labeled with the the ___________________. Example 1 - Graph a function Graph the function y = x + 1 with domain 1, 2, 3, 4, and 5. Step 1 Make an _____________________________ table. x y Step 2 Plot a point for each ___________________________ (x, y). Step 3 Draw a line to connect the points if needed. What is the range of this function? Example 2 - Graph a function Graph the function y = 2x - 2. Step 1 x Step 2 y Since the domain is not given, we choose values. A good rule is to choose two negative values, 0 and two positive values. Step 3 Draw a line to connect the points if needed. Page 1 What is the range of this function? Now You Try It! 1) Graph the function y = x + 2 with domain 1, 2, 3, 4, and 5 x y What is the range of this function? 2) Graph the function y = 2x + 1. x y What is the range of this function? Example 3 – Putting it all together. The admission for students to go to Water Works is $24 per person. The cost of the busses for the entire 7th grade is $450. a) Write an equation or rule that represents the function. b) Make a table that shows how much a trip for 50 students, 100 students, 150 students, 200 students, and 250 students would cost. e) What is the range? x Page c) Graph the application. Don’t forget: Title Label x and y axis with name Label values Decide if your line should be connected. d) What do you notice about the starting value? 2 y Now You Try It! ABC Package company charges a flat rate of ten dollars to box any item and then a charge of 5 dollars per pound to ship. a) Write an equation or rule that represents the function. b) Make a table that shows the cost of shipping a 5 pound, 10 pound, 15 pound, 20 pound and 25 pound package. x y c) Graph the application. d) What do you notice about the starting value? e) What is the range? Example 4 – The Vertical Line Test If you are looking at a graph and want to decide if it is a function, you can use the “vertical line test”. d) Why does the this test work????? 3 c) Function? b) Function? Page a) Function?