1. Today’s Agenda
 Attendance / Announcements
◦ Projects due
◦ No Quiz Friday (exam week)
◦ Need Graphing Calculators (TI-83,84,..)
 Section 3.1

2. Functions
A function is a rule
(think: operation)
that assigns an input
value to exactly one
specific output
f(x) can be thought of as “y”

3. Examples…before we really define
what a function is.
32 xy 32)( xxf
xxy 323
2
ttth 323)(
2
xy 3 xxg 3)(

4. A function is a rule (think: operation) that assigns
an input value to exactly one specific output
inputs outputsf(x)
Domain Range

5. Determine if each relation is a function or not…
9 4 1 0 1 4 9
3 2 1 0 - 1 - 2 - 3
“Functions need to be predictable!”

6. Determine if each relation is a function or not…
-2 -1 0 3 4 6 9
3 2 1 0 1 2 3
Since it is a function, it has a domain and range:
Domain (set of all inputs): { }
Range (set of all outputs): { }

7. Function Notation (p. 137)

8. Evaluating Functions
,2)(
2
xxxfif
)3(f
)3(f
)(tf
)3( xf

9. “The Difference Quotient”
The difference quotient for a
function f(x) is:
h
xfhxf )()(
Substitute, Subtract, and Simplify

10. h
xfhxf )()(
Find the difference quotient of: 53)( xxf

11. h
xfhxf )()(
Find the difference quotient of:
53)( xxf

12. h
xfhxf )()(
Find the difference quotient of:
1)(
2
xxf

13. Finding Domains of Functions
The domain of a function is the set of
values where the function is defined.
So, to find domains, we need to think
about where functions are NOT
defined!

14. Finding Domains of Functions
Red Flags
• Zero(s) in the denominator
• Negative under square root

15. Finding Domains of Functions

16. Finding Domains of Functions

17. Finding Domains of Functions

18. Classwork / Homework
Page 140
9 – 19 odd,
23 – 29 odd,
35 – 45 odd,
51