1. 3.2 (Day 2) Difference Quotient & Graphs of Functions

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

3. Ex 1) Find the difference quotient of

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

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

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

7. 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 Ex 4) Graph 1.0 1.2 1.9 2.0 2.2 2.9 3.0 xy 1 1 1 2 2 2 3

8. Greatest Integer Function Actual Table: x y

9. Homework #304 Pg. 179 45 – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even