1. Algebra II Honors—Day 8

2. Goals for Today Reminder—First Graded Homework Assignment (checked for accuracy)—due next Tuesday, Sept. 10 Essential Questions – New Material Classwork/Homework

3. Essential Questions What is a function and how do I determine if a relation is a function? How do I use function notation to evaluate a function? How do I determine a function’s domain and range from its equation or from its graph?

4. Notes A function is a relation that maps every x- value with exactly one y-value. In other words, if I tell you the x, you will always know the y based on the function definition. Vertical line test helps identify graphs as functions or not.

5. Functions Functions: {(3,6), (4, 22), (-8, 20), (6.5, 20)}—none of the x- values repeat. Each x is paired with only one y. Notice that it’s OK for the y-values to repeat. This is a function because if you tell me what x is, you will get a unique value of y by plugging in the value of x. This is a linear function.

6. Practice Function Notation Classwork

7. Domain and Range Domain—consists of all possible inputs for a function (the x-values or the independent variable values) Range—all of the outcomes that are possible for the given domain Some functions have limited domains and ranges. You will need to learn how to recognize domains and ranges from graphs.

8. Examples For linear equations: – Domain is all real numbers D: – Range is all real numbers R: This means that a line goes on and on forever. Every value of x gives a unique value of y, and every value of x and y are possible.

9. Domain and Range from Graphs Sometimes the domain and range are determined from the graph based only on what you see. – On this graph, the domain is (-3,3) and the range is (-9,0). Why????

10. Homework Domain and Range Handout—due tomorrow – Problems 1, 2, 3, 4, 7, 10, 11, 14 Quotable Puzzles—due Monday