1 4 Modeling with Functions IV Objectives v

1. 4 Modeling with Functions IV Objectives: v Use a function as a mathematical model. v Determine when a function is increasing, decreasing, or constant. v Use the vertical line test to determine whether a graph represents a function. MAFS. 912. F-LE. 1. 2

Terminology Mathematical Model An equation or graph that fits or approximates actual data. The model can be used to predict output values not in the table. Increasing Function Decreasing Function Constant Function MAFS. 912. F-LE. 1. 2

Mathematical Modeling The table shows the braking distance for an average vehicle. Police use the skid distance to find the speed of a vehicle. Plot the data What would you predict the speed of a car to be if the skid was 200 feet? MAFS. 912. F-LE. 2. 5

Mathematical Modeling The value of your lakefront home appreciates over time. You purchased your home for $85, 000. The value increases $1, 250 per year. Verbal – A statement of the definition of a function The value of the home is 1, 250 times the number of years added to 85, 000. Symbolic – equation MAFS. 912. F-LE. 1. 2

Mathematical Modeling The value of your lakefront home appreciates over time. You purchased your home for $85, 000. The value increases $1, 250 per year. Numeric – A picture -- like a table years 0 1 2 3 4 value Graphical – A graph If you keep the home for 8 years, how much will it be worth? $95, 000 MAFS. 912. F-LE. 1. 2

Increasing, Decreasing, Constant MAFS. 912. F-LE. 1. 2

Functions - Vertical Line Test A function will only touch a vertical line at one point at a time. MAFS. 912. F-LE. 1. 2