1. Precalculus
Day 36

2. Precalculus
Day 36

3. Precalculus
Day 36

4. Knight’s Charge a. cos(60o) = ____ RA:______ Quad:_____
NO CALCULATOR:
a. cos(60o) = ____
RA:______ Quad:_____
b.sin( 𝜋 4 ) = _____
c. tan(300o) = ___
d. cot( 45o) = ____
e. csc(270o) = ___
f. sec ( 5𝜋 4 ) = _____
g. sin(-150o) = ___
h. tan(𝜋 ) = _____

5. Domain and Range
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Domain and range can be seen clearly from a graph, as well as from a function.

6. Domain and Range from a graph
domain  x rangey

8. Domain and Range from a graph
domain  x rangey

9. Domain and Range from a graph
domain  x rangey

10. Domain and Range from a graph
domain  x rangey

11. Increasing/Decreasing Intervals
Another way of saying that a graph is going up is that its slope is positive or that the function is INCREASING. If the graph is going down, then the slope will be negative, and we say the function is DECREASING. NOTE: A function that does not have a constant slope can be increasing on a certain interval and decreasing on another interval.

12. Increasing and Decreasing Intervals
Find all relative minima and maxima.
2nd TRACE 3 and 4

13. Increasing and Decreasing Intervals
Describe the increasing and decreasing behavior.
The function is decreasing on the interval
increasing on the interval

14. The function is decreasing over the entire real line.
Increasing and Decreasing Intervals
Describe the increasing and decreasing behavior.
The function is decreasing over the entire real line.

15. Increasing and Decreasing Intervals
Describe the increasing and decreasing behavior.
The function is increasing on the interval
constant on the interval
decreasing on the interval

16. Group Practice Where is each function increasing and decreasing?

17. Group Practice

18. Relative Max and Min

19. Relative Max and Min

20. Relative Max and Min

21. Relative Max and Min

22. Relative Max and Min

23. Function Type: Even, Odd, or Neither
Even function
A function f(x) such that f(x) = f(–x)
This means the graph of f(x) will have a line of symmetry at the y-axis

24. Even Functions

25. Function Type: Even, Odd, or Neither
Even function
A function f(x) such that f(x) = f(–x)
This means the graph of f(x) will have a line of symmetry at the y-axis
Odd function
A function f(x) such that f(x) = –f(–x)
The means the graph of f(x) will have rotation symmetry about the origin

26. Function Type: Even, Odd, or Neither

27. Function Type: Even, Odd, or Neither
Even function
A function f(x) such that f(x) = f(–x)
This means the graph of f(x) will have a line of symmetry at the y-axis
Odd function
A function f(x) such that f(x) = –f(–x)
The means the graph of f(x) will have rotation symmetry about the origin
A function can be neither even nor odd

28. Are the following functions even, odd, or neither?

29. EvaluAting Functions from Graph