1. FUNCTIONS
What are they?

2. Goal Learn general properties that apply to all types of functions
Transform a function so that its graph fits real-world data
Obtain goals
Graphically
Algebraically
Numerically
Verbally

3. Overview (shooting arrow)
Graphically 
Algebraically: y = −4.9x2 + 20x + 5
Numerically: x (s) y (m)
0 5.0
Verbally: -4.9 is constant pertaining to gravitational acceleration, 20 is initial velocity, and 5 represents initial height of arrow.

4. Cup of Coffee
How does the temperature of a cup of coffee relate to the time it sits???????
There is one and only one temperature at any one given time, sooooooooooo
Temperature is a function of time!

5. Understanding Coffee Algebraically Numerically y = 20 + 70(0.8)x.
x (min) y (°C)
0 90

6. Verbal Coffee Mathematical Model
Function that is used to make predictions and interpretations about something in the real world
Temperature depends on Time? Or time depend on Temperature?
Temp is Dependent Variable
Temp depends on time it has been cooling
Time is Independent Variable
Cannot change time by changing temp!

7. Domain/Range
Domain: The set of values the independent variable of a function can have is called the Domain
Range: The set of values of the dependent variable corresponding to the domain is called the range of the function
The horizontal line at 20°C is called an asymptote. “Not due to coincide.” End behavior of the graph.
ALWAYS PLOT INDEPENDENT VARIABLE ON X-AXIS AND DEPENDENT VARIABLE ON Y-AXIS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

8. Example 1
The time it takes you to get home from a football game is related to how fast you drive. Sketch a reasonable graph showing how this time and speed are related. Give the domain and range of the function.

9. Final Graph Domain: 0 ≤ speed ≤ speed limit
Range: time ≥ minimum time at speed limit