1. Lecture: 1D Pre AP & GT Precalculus
Parent Functions
Lecture: 1D Pre AP & GT Precalculus

2. Function Notation
When referring to the output of a function, we typically use f(x) to denote the y-value output associated with an inputted x-value.
This notation is due to Leonhard Euler (pronounced: Oiler)

3. Constant Function

4. Linear Function

5. Review: Linear Functions

6. Linear Function Example
Find the equation of the linear function through the points (-1,2) and (3.-4)
Be Careful not to do too much algebra

7. Quadratic Functions

8. Square Root Function

9. Average Rate of Change

10. Average Rate Example
What is the Average Rate of Change of the general quadratic between x=-1 and x=2

11. Average Rate of Change Example
On the Westpark Tollway, one tollbooth is located at mile marker 52 and another is located at 62. The elapsed time between tollbooths for a driver is 7.5 minutes? What is the driver’s average speed on that interval?
Hint: Distance is a function of time

12. Average Rate of Change Example
Reflection: What does this mean?
According to the mean value theorem from calculus, averaging a speed of 80 means that at one point on the interval, the driver was going 80 mph. Since the speed limit
is less than 80 mph, cops can give tickets from EZ Tag Data

13. Piecewise Function
(definition) A function whose definition is given differently on disjoint subsets of its domains.
Notation:
Absolute Value Example

14. Graph this function:

15. Piecewise Function
Reflection: Why is the notion of disjoint domain subsets important in the definition of a piecewise function?
If the function value was doubly defined for any point on the domain, it would fail the vertical line test and not be a function

16. Greatest Integer Function
Also called a Step Function or Floor Function
(notation) [[x]]
(verbal definition) the function which outputs the greatest integer less than or equal to the input.

17. Greatest Integer Examples
What is [[π]]?
[[π]] = 3
What is [[-π]]?
[[− π]]= − 4

18. Step Functions
Reflection: What are some real life situations that can be modeled by a step function?
Digital Signals, Power Switches