1. Functions (but not trig functions!)
Objectives: Be able to…
-Identify, evaluate and find the domain of functions.
-Determine where a graph is increasing, decreasing or constant
-Find the extrema of a function
-Determine if a function is even, odd or neither
TS: Make decisions after reflection and review

2. Formal Definition
A function, f, from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs) and the set B contains the range (or the set of outputs).

3. Is it a function? What is the domain & range?

4. Is it a function? What is the domain & range?x 2 3 4 5 y 11 10 8 1

5. Is it a function?

6. Find the domain of each

7. Find the domain of each

8. Increasing, Decreasing or Constant
Increasing Interval:
For any x1 and x2 in the interval x1 < x2 implies f(x1) < f(x2)
Decreasing Interval:
For any x1 and x2 in the interval x1 < x2 implies f(x1) > f(x2)
Constant Interval:
For any x1 and x2 in the interval x1 < x2 implies f(x1) = f(x2)

9. Find the open intervals of x over which the functions are increasing, decreasing or constant.
y=|x2 – 4|

10. Extrema (Absolute & Relative Maximums & Minimums)
Using your calculator approximate the extrema for f(x) = -x3 + x
Using your calculator approximate the extrema for
Using your calculator approximate the extrema for y = |x – 3| + |x + 4| - |x+2|

11. Even & Odd Functions Even functions:
Functions which have y-axis symmetry
f(-x) = f(x)
Odd Functions:
Functions which have origin symmetry
f(-x) = – f(x)

12. Test algebraically to see if each function is even, odd or neither
Test algebraically to see if each function is even, odd or neither. Then verify graphically.
g(x) = x3 – x ) h(x) = x2 + 1
3) f(x) = x3 – 1

13. Closure: See if you can think of answers to these two questions.
Find two non-polynomial even functions. They can’t both use the same parent.
Draw a picture of an object that has both origin and y-axis symmetry. Can you make one that is a function?