1. Graphs of Functions (Part 2) 2.5 Graphing calculator day

2. POD Give the new form of y = f(x) under the following transformation: vertical shift down 2 horizontal shift right 3 horizontal compression by 4

3. POD Give the new form of y = f(x) under the following transformation: vertical shift down 2 horizontal shift right 3 horizontal compression by 4

4. Piecewise functions– another go Graph this function on your calculator. The trick to getting a sound graph is to make sure x is the first term in the typed interval.

5. Piecewise functions– another go, on the 84

6. Piecewise functions– another go, on CAS

7. Piecewise functions– another go What are the domain and range? Where are the points of discontinuity? How could we change the function so that it is continuous?

8. The greatest integer function Suppose you have a job making widgets. Okay, not widgets– think of something else. You’re paid for each completed item, so if you make 25 ½ of them, only 25 are credited. This rounding down to the nearest integer is called the “rounding down” or greatest integer function. You have it on the parent function sheet.

9. The greatest integer function Each value of x is rounded down to the next integer. This is also called the floor function. The notation looks like What does the graph look like? See how this could be labeled a “step function?”

10. The greatest integer function Graph on the 84’s or on CAS. The trick is to keep track of which endpoints are open and closed. What are the domain and range? Where is the function discontinuous?

11. The greatest integer function Now, let’s transform this bad boy. Stretch it vertically by 4 and shift left by 2. What is the equation and what does the graph look like?

12. The greatest integer function Now, let’s transform this bad boy. Stretch is vertically by 4 and shift left by 2. What are the domain and range? Where is it discontinuous?

13. The ceiling function In addition to the floor function, there is something called the ceiling function. In this function, each value of x is rounded up to the next integer. The notation looks like What does the graph look like?

14. The ceiling function The ceiling graph looks like it’s simply shifted up by 1 from the floor graph. But something else is going on– what is it?

15. Absolute value Moving beyond the simple… Before graphing this, see if you can anticipate what it looks like. y = |x 2 - 4|

16. Absolute value y = |x 2 - 4| Compare this to y = x 2 – 4. What do you think changes?

17. Absolute value y = |x 2 - 4| Compare this to y = x 2 – 4. What do you think changes? The values for y will not be negative– they reflect back over the x axis.

18. Absolute value Sometimes solving an equation algebraically is just too tough– use the graph as another tool. Solve this by graphing each side separately.

19. Absolute value Then what?

20. Absolute value Then what? Calculate intersections. At x = ±15.52 and ±2.80

21. Absolute value Final answer: (-∞, -15.52)U(-2.80, 2.80)U(15.52, ∞)