1. Function Notation II. Lesson notes As we learned in using patterns, some relations or sets of ordered pairs can be represented by an equation. When the set of ordered pairs satisfies the definition for a function we can use function notation.

2. Example 1: For each function, evaluate A. B.

3. Dependent and Independent Variables: In the notation f(x), f is the name of the function, x is the input of the function and, when we evaluate for some x, that is the output. The input and output in a function are also known as the independent and dependent variables.

4. Example 2: Graph each function. A. The diagram shows the maximum recommended heart rate for women by age.

5. B. The maximum recommended heart rate h for men is a function of age a and can be calculated with h(a) = 214 – 0.8a.

6. Function Rule: The algebraic expression used to define a function is called the function rule. To write a function rule, first identify the independent and dependent variables. Example 3: Application: The Japanese bullet train that travels from Tokyo to Kyoto averages about 156 km/h. The distance fro Tokyo to Kyoto is 380 km. A. Write a function to represent the distance remaining on the trip after a certain amount of time. B. What is the value of the function for an input of 1.5 and what does it represent?

11. 7. In a certain country the fines for speeding in a school zone are $160 plus an additional $4 for every mile per hour over the speed limit. A. Write a function to represent the speeding fines. __________________________________________________ B. What is the value of the function for an input of 8 and what does it represent? __________________________________________________