Compare Functions Written in Different Forms Verbal, Equations, Tables and Graphs

Focus 6 - Learning Goal #1: Students will understand and explain the difference between functions and non-functions using graphs, equations, and tables. 4 3 2 1 In addition to level 3.0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas.   The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables. Compare properties of a function to a non-function. The student will be able to model and evaluate functions and non-functions. Use graphs, equations, and tables to determine functions and non-functions. With help from the teacher, the student has partial success with level 2 and 3 elements. Even with help, students have no success with the functions.

There are many ways a function can be communicated There are many ways a function can be communicated. Here are 4 main ways: Verbal Model: Mariah opened her savings account with $1,200. Each month she adds $50. Equation: y = 1200 + 50x Where y represents the amount in Mariah’s account and x represents the number of months she made the deposit. Table: Graph: Months (x) Amount in account (y) $1,200 1 $1,250 2 $1,300 3 $1,350 4 $1,400 5 $1,450 Each one of these formats communicate the same information about Mariah and her savings account.

Compare Functions It’s hard to compare two functions when they are written in different formats. Gas mileage of Car #2. Gas mileage of Car #1 is 16 miles per gallon.

Compare Functions How can we determine which car has the better gas mileage? We can either graph them both or write them both as a verbal statement. It may be easier to change the graph of car #2 to a verbal statement. How many miles can car #2 go on a gallon of gas? Car #2 gets 20 miles per gallon. If car #1 gets 16 miles per gallon and car #2 gets 20 miles per gallon, which car gets the better gas mileage?

Kip and Joan are members at different fitness clubs… Who has the better deal for going to the gym for only one week? Kip’s cost for 1 week = Joan’s cost for 1 week = Who has the better deal after 8 weeks of having the membership? Kip’s cost for 8 weeks = Joan’s cost for 8 weeks = Kip’s Gym Membership Joan’s membership fee is $50 then she pays $10 per week. $40 $60 $180 $130

Video rental LATE fees for 2 different stores. Which store is cheaper for 2 days late? Store 1 = Store 2 = Which store is cheaper for 10 days late? Store 1 Store 2 y = 1.25x + 1 Where y is the total late fee and x is the number of days late. Days Late Fee 1 $1.50 2 $3.00 4 $4.50 5 $6.00 $3.00 $3.50 $15.00 $13.50