1. Characteristics of Polynomials: Domain, Range, & Intercepts
Daily Questions…….
What is interval notation?
3. What is the domain & range of a function?
4. How do I find the intercepts of a functions graphically and algebraically?

2. How do we write in interval notation?
x < 2….
when you want include use a bracket [
when you want to exclude use a parenthesis (
Let’s draw a number line first….

3. Draw a number line first….
Let’s do another type….
Draw a number line first….

4. Domain Range all the x-values Read the graph from left to right
all the y-values
Read the graph from bottom to top

5. What is the domain of f(x)?
Ex. 1
(2,4)
(-1,-5)
(4,0)
y = f(x)
Domain

6. Ex. 2: What is the range of f(x)?
(2,4)
(-1,-5)
(4,0)
y = f(x)
Range

7. With polynomials…. The DOMAIN is always All Reals, ,
The RANGE will be:
All Reals, ,
Lower Boundary to infinity,
Negative infinity to Upper Boundary,

8. Zeros/x-intercepts/Solutions/Roots Where the graph crosses the x-axis
What’s a zero?
Zeros/x-intercepts/Solutions/Roots
Where the graph crosses the x-axis

9. Where the graph crosses the x-axis. Also called zeros.
Analyze the Graph of a Function
x-intercepts
Where the graph crosses the x-axis. Also called zeros.
Zeros: 1, 5

10. X-Intercepts: (-2, 0) (-2, 0) (3,0)
Zeros, Roots:
x = -2, -2, 3

11. X-Intercepts: (-1,0)(1,0)(2,0)
Zeros, Roots
x = -1, 1, 2

12. y-intercepts
Where the graph crosses the y-axis

13. y-Intercept: (0,-12)

14. y-Intercept: (0,2)

15. Y- int: (0, -1) # of zeros: 4 Y- int: (0, 15) # of zeros: 2
Find the y-intercepts & number of zeros: a) b)
Y- int: (0, -1)
# of zeros: 4
Y- int: (0, 15)
# of zeros: 2

16. All reals All reals (-2,0)(-2,0)(1,0) (0, -4) Find the following
Domain:
Range:
3. x-intercepts:
4. y-intercepts:
All reals
All reals
(-2,0)(-2,0)(1,0)
(0, -4)

17. All reals [-4, ∞) -2, 2 (0, -4) Find the following Domain: Range:
3. Zeros:
4. y-intercepts:
All reals
[-4, ∞)
-2, 2
(0, -4)

18. Increasing
Decreasing
Constant
This is a piecewise function

19. Increasing and decreasing are stated in terms of domain
Ex.
(-, -1)
(-1, 1)
(1, )
increasing
decreasing
increasing
(-1,2)
(1,-2)

20. Increasing and decreasing are stated in terms of domain
Ex.
Increasing and decreasing are stated in terms of domain
(-, 0)
(0, 2)
(2, )
constant
increasing
decreasing
(0, 1)
(2, 1)

21. Determine the intervals over which the function is increasing and decreasing…

22. Relative Minimum & Maximum Values (direction change)
Relative Minimum: all of the lowest points
Relative Maximum: all of the highest points

23. Absolute Minimum & Maximum
Absolute Minimum: the lowest point
Absolute Maximum: the highest point

24. Relative maximum
Relative minimum

25. All reals All reals -2, -2, 1 (0, -4) none max: (-2, 0) min: (0, -4)
Find the following
Domain:
Range:
3. Zeros:
4. y-intercepts:
5. Absolute Max/Min:
6. Relative Max/Min:
7. Increasing:
8. Decreasing:
All reals
All reals
-2, -2, 1
(0, -4)
none
max: (-2, 0) min: (0, -4)

26. All reals [-4, ∞) -2, 2 (0, -4) min: (0, -4) min: (0, -4) (0, ∞)
Find the following
Domain:
Range:
3. Zeros:
4. y-intercepts:
5. Absolute Max/Min:
6. Relative Max/Min:
7. Increasing:
8. Decreasing:
All reals
[-4, ∞)
-2, 2
(0, -4)
min: (0, -4)
min: (0, -4)
(0, ∞)
(-∞, 0)