Polynomial Functions on a Graphing Calculator
Properties of Polynomial Functions
Cubic Functions: [pic]
1. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Sketch the graphs in the space provided below each equation.
a) [pic] b) [pic] c) [pic] d) [pic]
2. How are these four graphs similar?____________________________________________
3. How are these four equations the same?________________________________________
4. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Sketch the graphs in the space provided below each equation.
a) [pic] b) [pic] c) [pic] d) [pic]
5. How are these four graphs similar?____________________________________________
6. How are these four equations the same?________________________________________
7. Complete the table below by referring to the graphs in #1 and #4.
| | |Degree: even |Number of Turning |Leading Coefficient: | | |
| | |or odd |Points | |End behaviour: |End behaviour: |
|Function |Degree | | |+ or - ? |as [pic] |as [pic] |
|1. a) | | | | |[pic] |[pic] |
|1. b) | | | | | | |
|1. c) | | | | | | |
|1. d) | | | | | | |
|4. a) | | | | | | |
|4. b) | | | | | | |
|4. c) | | | | | | |
|4. d) | | | | | | |
8. Describe how the graphs of cubic functions for which a is positive differ from those for which
a is negative._____________________________________________________________
Quartic Functions: [pic]
9. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Sketch the graphs in the space provided below each equation.
a) [pic] b) [pic] c) [pic] d) [pic]
10. How are these four graphs similar?____________________________________________
11. How are these four equations the same?________________________________________
12. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Sketch the graphs in the space provided below each equation.
a) [pic] b) [pic] c) [pic] d) [pic]
13. How are these four graphs similar?____________________________________________
14. How are these four equations the same?________________________________________
15. Complete the table below by referring to the graphs in #9 and #12.
| | | | |Leading Coefficient: | | |
| | |Degree: even or odd |Number of Turning Points| |End behaviour: |End behaviour: |
|Function |Degree | | |+ or - ? |as [pic] |as [pic] |
|9. a) | | | | |[pic] |[pic] |
|9. b) | | | | | | |
|9. c) | | | | | | |
|9. d) | | | | | | |
|12. a) | | | | | | |
|12. b) | | | | | | |
|12. c) | | | | | | |
|12. d) | | | | | | |
16. Describe how the graphs of quartic functions for which a is positive differ from those for which a is negative.
______________________________________________________________________
17. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Sketch the graphs in the space provided below each equation and then complete the table below.
a) [pic] b) [pic] c) [pic]
d) [pic] e) [pic] f) [pic]
g) [pic] h) [pic]
| | | | |Leading Coefficient: | | |
| | |Degree: even or odd |Number of Turning Points| |End behaviour: |End behaviour: |
|Function |Degree | | |+ or - ? |as [pic] |as [pic] |
|17. a) | | | | |[pic] |[pic] |
|17. b) | | | | | | |
|17. c) | | | | | | |
|17. d) | | | | | | |
|17. e) | | | | | | |
|17. f) | | | | | | |
|17. g) | | | | | | |
|17. h) | | | | | | |
18. The maximum number of turning points in the graph of a polynomial function with degree 8 is
__________. The maximum number of turning points in the graph of a polynomial function
with degree 9 is __________. The maximum number of turning points in the graph of a
polynomial function of degree n is __________.
19. Polynomials with EVEN degree have end behaviours that are _________________________
Polynomials with ODD degree have end behaviours that are __________________________
20. State the end behaviours of a function with a degree that is:
a) even and has a positive leading coefficient [pic]
b) even and has a negative leading coefficient ______________________________________
c) odd and has a positive leading coefficient ______________________________________
d) odd and has a negative leading coefficient ______________________________________
21. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Graph each function and complete the chart on the next page.
a) [pic] b) [pic] c) [pic]
d) [pic] e) [pic] f) [pic]
g) [pic] h) [pic]
|Function |Degree of Polynomial |Number of Zeroes |
|a) [pic] | | |
|b) [pic] | | |
|c) [pic] | | |
|d) [pic] | | |
|e) [pic] | | |
|f) [pic] | | |
|g) [pic] | | |
|h) [pic] | | |
22. Complete the following chart stating the minimum and maximum number of zeroes possible for a polynomial function with each given degree.
|Degree |Minimum number of zeroes |Maximum number of zeroes |
|5 | | |
|6 | | |
|7 | | |
|8 | | |
|n (odd) | | |
|n (even) | | |
23. Refer to the graphs of the following polynomial functions to complete the chart below.
a) b) c)
[pic] [pic] [pic]
| | |Leading Coefficient: | | | |
| | |+ or - ? |End behaviour as [pic] |End behaviour as [pic] |Number of Turning Points |
|Function |Cubic/Quartic? | | | | |
|23. a) | | |[pic] |[pic] | |
|23. b) | | | | | |
|23. c) | | | | | |
24. Describe the end behaviour of each polynomial function by referring to the degree and the leading coefficient.
| |End behaviour: as [pic] |End behaviour: as [pic] |
|Function | | |
|a) [pic] |[pic] |[pic] |
|b) [pic] | | |
|c) [pic] | | |
|d) [pic] | | |
|e) [pic] | | |
|f) [pic] | | |
Quintic Functions: [pic]
25. Using a graphing calculator, adjust the window settings so that the intervals are [pic] and [pic] on the axes. Sketch the graphs in the space provided below each equation.
a) [pic] b) [pic]
c) [pic] d) [pic]
26. How is the graph of a quintic function similar to the graph of a cubic function?
______________________________________________________________________
27. Complete the table below by referring to the graphs in #25.
| | | | |Leading Coefficient: | | |
| | |Degree: |Number of Turning Points|+ or - ? |End behaviour: |End behaviour: |
|Function |Degree |even or odd | | |as [pic] |as [pic] |
|25. a) | | | | |[pic] |[pic] |
|25. b) | | | | | | |
|25. c) | | | | | | |
|25. d) | | | | | | |
28. Describe how the graphs of quintic functions for which a is positive differ from those for which a is negative.
______________________________________________________________________
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- recognizing linear functions from words
- algebra i mip
- scientific notation worksheet
- pre calculus parametrics worksheet 2
- pre calculus unit 4 1st 9 weeks
- math test—no calculator the sat suite of
- computer mathematics and the graphing calculator
- polynomial functions on a graphing calculator
- polynomial patterns learning task
- first exam practice sheet
Related searches
- best graphing calculator for calculus
- windows graphing calculator app
- how to identify functions on a graph
- finding polynomial functions calculator
- zeros of polynomial functions calculator
- find six trigonometric functions on a calculator
- graphing on a coordinate plane
- identifying polynomial functions calculator
- roots of polynomial functions calculator
- find correlation on a graphing calculator
- graphing inequalities on a number line pdf
- polynomial functions calculator