King/Halling Algebra 2011-2012 Function Rules King/Halling Algebra 2011-2012

AIM How do we write function rules from a table of values? How can we use these function rules to explain a relationship between two variables?

DO NOW Prove whether or not the following relation is a function using at least two different methods. Possible ways of proving this include using the ordered pairs, function mapping, the vertical line test, etc. {(2,3), (0,6), (3,-5), (-4,-1), (2,5), (-1,2)}

Functions Review Input Output Typically the x variable Also known as independent variables; domain Cannot repeat or the relation is not a function Typically the y variable Also known as dependent variables; range Can repeat, even if the relation is a function Input Output Function Rule

Function Rules Gallons of Gas Used Miles Driven 1 23 2 46 3 69 4 92 Use the table at the right to create a function rule defining the given function. Be sure to define your variables. Gallons of Gas Used Miles Driven 1 23 2 46 3 69 4 92

HOW TO G = gallons of gas used M = miles driven M = 23G For every gallon of gas this car uses, it is able to drive 23 miles. The car gets 23 mpg.

Using the Calculator 40 1 35 2 30 3 25 Doughnuts Purchased Money ($) 40 1 35 2 30 3 25 Sometimes it’s difficult to write a rule for the given function We can use the calculator to help us define difficult functions

Using the Calculator Follow the steps on the calculator guidelines worksheet You may work in groups or independently

EXIT TICKET Number of Cakes Sold Money ($) -150 2 -100 4 -50 6 Create a function rule describing the table at the right What was the initial cost of the business? How much do they make per cake? (**HINT: Be Careful**) Number of Cakes Sold Money ($) -150 2 -100 4 -50 6