GRAPH OF POLYNOMIAL FUNCTIONS Grade 10.pptx

GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10POLYNOMIAL GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade 10FUNCTIONS Grade 10GRAPH OF POLYNOMIAL FUNCTIONS Grade

1. GRAPH OF POLYNOMIAL FUNCTIONS

2. IN A NUTSHELL The graph of a polynomial function has the following properties.   1. The domain is the set of all real numbers . The x and y –intercepts are both zeroes. 2. a. If n is odd; the range is the set of all real numbers and the graph is symmetric with respect to the origin.

3. IN A NUTSHELL The graph of a polynomial function has the following properties.   2. b. If n is even; the graph is symmetric with the y- axis and If a< 0, then the range is (- If a> 0, then the range is [0, + )  

4. IN A NUTSHELL The graph of a polynomial function has the following properties.   3. The graph of can be obtained by inverting or reflecting the graph of over the x-axis.  

5. IN A NUTSHELL The graph of a polynomial function has the following properties.   4. Compared to the graph where =1   the graph where 1 is narrower. the graph where Q < < 1 is wider.  

6. The graph of are both symmetric with respect to the origin.   Domain: R (Real Numbers) Range: R (Real Numbers)

7. The graph of are both symmetric with respect to the y-axis.   Domain: R (Real Numbers) Range: [0, + )  

8. EXAMPLE 1.   The graph of is symmetric with respect to the y-axis.   Domain: R (Real Numbers) Range: (-  

9. EXAMPLE 1.   The graph of is symmetric with respect to the origin.   Domain: R (Real Numbers) Range: R (Real Numbers)

10. 1.   The graph of is symmetric with respect to the y-axis.   Domain: R (Real Numbers) Range: [0, + )   2.   The graph of is symmetric with respect to the origin.   Domain: R (Real Numbers) Range: R (Real Numbers)

11. HORIZONTAL AND VERTICAL TRANSLATIONS

12. EXPLORE: GRAPH THE FOLLOWING 1. and -3   2. and  

13. Compared to the graph of   The graph of is translated (or shifted). a. units up if 0 and b. units down if 0. This is called the vertical translation.  

14. Compared to the graph of   2. The graph of a. units to the right if h 0 and b. units to the left if h 0. This is called the horizontal translation.  

15. Compared to the graph of   3. The graph of + shows a combination of these translation  

16. EXAMPLE: Sketch the graph. Identify the domain and range. 1.   2.  

17. EXAMPLE: Sketch the graph. Identify the domain and range. 1. -6   2.   3.  

18. INTERCEPTS

19. EXAMPLE: Sketch the graph. 3.   2.   1.  

20. EXAMPLE: Find the x and y intercept. 1.   x -intercept= 0, 1, -2 y-intercept= 0

21. EXAMPLE: Find the x and y intercept. 2.   x -intercept= 0, -3 y-intercept= 0

22. EXAMPLE: Find the x and y intercept. x -intercept= -1, 2, 3 y-intercept= 6 3.  

23. Multiplicity of a Zero and Turning Points

24. The multiplicity of a zero of a polynomial function is a helpful strategy to determine whether the graph crosses or is tangent to the x–axis at each x–intercept.

25. Multiplicity tells how many times a particular number is a zero or root for the give polynomial.

26. The turning points of a graph occur when the function changes from decreasing to increasing or from increasing to decreasing values. The number of turning points in the graph of a polynomial function with degree n is strictly less than the degree of the polynomial or at most (n – 1).

27. The graph of polynomial function is continuous , smooth , and has rounded turns.

28. Examples: Given the polynomial functions, describe or determine the following and sketch the graph. a. leading term b. end behaviors c. x-intercepts points on the x-axis d. multiplicity of roots e. y-intercept point on the y-axis f. number of turning points g. sketch