1. 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

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

3. 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

4. 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

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.
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

6. Increasing, Decreasing, Constant
MAFS.912.F-LE.1.2

7. Functions - Vertical Line Test
A function will only touch a vertical line at one point at a time.
MAFS.912.F-LE.1.2