1.4 Modeling with Functions IV Objectives: Use a function as a mathematical model. Determine when a function is increasing, decreasing, or constant. 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 A function whose output value (𝑦) increases left to right. Decreasing Function A function whose output value (𝑦) decreases left to right. Constant Function A function whose output value (𝑦) is constant (horizontal). 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. Which variable is a function of the other? 𝑠𝑝𝑒𝑒𝑑 𝑖𝑠 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑜𝑓𝑠𝑘𝑖𝑑 𝑑𝑖𝑠𝑡. 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 𝒗=𝟏𝟐𝟓𝟎𝒚+𝟖𝟓𝟎𝟎𝟎; 𝑣=𝑣𝑎𝑙𝑢𝑒, 𝑦=𝑦𝑒𝑎𝑟𝑠 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 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