1. Sec. 2.2
Functions

2. Function
A relation in which each element of the domain is paired with exactly one element in the range.

3. x values
y values
inputs
outputs
independent
dependent
Domain
Range

4. P. 185 Note function in boxes
Each element in A must be matched with an element in B.
Some elements in B may not be matched with any element in A.
2 or more elements of A may be matched with the same element of B.
4) An element in A (the domain) cannot be matched with two different elements in B.

5. What cannot happen A B 10 1 11 2 12 13 3 14 4 15

6. P. 186 Four ways to represent a Function
Verbally
Numerically
Graphically
Algebraically

7. Ex. Are the following functions?
(1, 2)(4, 5)(-6, 3)
(4, 2)(4, 3)(5, 6) x y c) d) x y 4 3 5 2 -3 1 5 2

8. e) 5 3 6 4 2 f) -1 -2 -3 5 6

9. Remember
Domain
Set of all values taken on by the independent variable x.
Range
Set of all values taken on by the dependent variable y.

10. To determine if an equation represents y as a function of x
Solve for y in terms of x
If there is only 1 possible answer that you would get for any value of x you input then yes it is a function.
If there is more than one possible answer you would get out then no it is not a function.

11. Ex. 2
x2 + y = 1
-x + y2 = 1 Ex
a) 3x2 + 2y = 6
b) x2 + y2 = 6

12. Function Notation Input Output Equation x f(x) f(x) = x2 + 2x - 5
Read f of x
Same as y
f is the name of the function
f(x) is the value of the function at x.

13. Ex
Find f(-2)
for f(x) = x2 + 2x – 5
Find f(3)
Find f(x + 1)

14. Look at Ex. 3 p. 190
Note f(x + 2) is not equal to g(x) + g(2)

15. Assignment
P. 195
1-8, odd, 37, 39,