1. 3.2 Functions (Day 1)
Today’s Date:
11/1/17

2. Functions
Relation: any set of ordered pairs (x, y) Domain: set of x-values Range: set of y-values Function: relation where x-values don’t repeat On a graph, it passes the vertical line test Written:

3. Ex 1) Relation: {(–1, 0), (0, –1), (1, 0)}
Domain: { –1, 0, 1}
Range: { –1, 0}
Function?
YES! (x’s don’t repeat)
Ex 2) Is the relation a function?
p = {(x, y) │ x = –2}
No! Fails vertical line test!
Don’t repeat yourself!

4. Finding the domain & range of an equation:
Domain: look for any restrictions on x
(y must be real)
x under radical
x in denominator of fraction

5. Finding the domain & range of an equation:
Range: look for any restrictions on y
(using known domain)
Draw a quick sketch if need to or use graphing calculator

6. Ex 3) Find domain & range of
Range: y is only positive
(square of negative is positive)
All Real Numbers
Interval Notation:

7. Ex 4) Find D & R of Domain: term under radical must be ≥ 0
Range: under radical ≥ 0

8. Find:
Ex 5)
Ex 6)
Ex 7)
Ex 8)

9. Homework
#303 Pg – 43 odd

10. 3.2 (Day 2) Difference Quotient & Graphs of Functions
Today’s Date:
11/1/17

11. Difference Quotient
(used in Calculus to study tangent lines to curves)

12. Ex 1) Find the difference quotient of

13. Ex 2) Sketch the graph of Pass the vertical line test? Yes! Function!-2 -1 1 2 3 4 5
│-2 – 2│
│-1 – 2│
│0 – 2│
│1 – 2│
│2 – 2│
│3 – 2│
│4 – 2│
│5 – 2│ 4 3 2 1
Pass the vertical line test?
Yes!
Function!

14. Ex 3) Determine if function:
No! It doesn’t pass the vertical line test.

15. Greatest Integer Function:
Greatest integer ≤ x
AKA Floor Function

16. Ex 4) Graph It’s a function, so must pass vertical line test
Plug in positive decimal values ≥ 1 to get a feel
then fill in pattern, including negatives
It’s a function, so must pass vertical line test y x x y
1.0
1.2
1.9
2.0
2.2
2.9
3.0 1 2 3

17. Homework
#304 Pg – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even