1. Unit 3
Functions

2. 4.1
What is a function?

3. What is a function?
Relation in which each element of the domain (x) is paired with exactly one element from the range [f(x)].

4. What is a function? For every x there is only exactly one y
X can’t repeat

5. How do we express functions
Verbally
Last summer I made $10.00 per hour.

6. How do we express functions
Numerically
Table/t-chart
Time (hours)
Pay (dollars) 5
50.00 12
120.00 25
250.00 30
300.00 40
400.00

7. How do we express functions
Algebraically
p = 10h

8. How do we express functions
Graphically
Pay ($)
Time (hours)

9. Domain
Independent variable
X variable
Input of the function

10. Range
Dependent variable
y variable
Output of the function

11. Evaluating a function:
A function has a value for every value in its domain
“x” represents the domain (input)
F(x) represents the range (output)
Function notation:
f(x)
g(x)
h(x)

12. Functional Notation: f(x), g(x), h(x) …
g(x) = -x2 + 4x + 1
g(2) 5
g(-3)
-20
g(t)
-t2 + 4t + 1
g(x + 2)
-(x + 2)2 + 4(x+2) + 1
-(x2 + 4x + 4) + 4x
-x2 - 4x x
-x2 +5

13. Functional Notation cont:
11/4
f(0)
Undefined
f(x + 1)

14. Piecewise Functions
f(7)
f(-2)
f(-5)
f(1)

15. Determine the domain of a function

16. Find the domain: S: {(-3,0),(-1,4),(0,2),(2,2),(4,-1)}
g(x) = -3x2 +4x +5
x   (true for all polynomials)
{x  | x ≠ -5}
{x  | x ≥ 3}
{r  | r > 0}
{r  | r ≠ 1, -.5}

17. Classwork Section 4.1
Pg :
#14-26 even
#36-46 even, 55, 59, 61