Leading Coefficient Test of polynomial function.pptx

This topic will help the students to determine the end behavior of the graph of a polynomial function.

1. directions Answer what is asked for each item and observe the given graphs. The first one is done for you.

2. Leading term: a n x n where a n ≠ 0 Leading coefficient: a n ˃ 0 → positive a n < 0 → negative Degree : even or odd

3. Polynomial function: y = x 3 – 7x + 6 Leading term: x 3 Leading coefficient: 1 → positive Degree : odd

4. Polynomial function: y = -3x 3 - 2x 2 + 8x Leading Term: __________ Leading Coef : ______________ Degree : __________ -3x 3 -3 → negative Odd

5. Polynomial function: y = x 4 – 3x 2 – 3 Leading Term: __________ Leading Coef : ______________ Degree : __________ x 4 1 → positive Even

6. Polynomial function: y = -3x 2 – 6x + 4 Leading Term: __________ Leading Coef : ______________ Degree : __________ -3x 2 -3 → negative Even

7. Polynomial function: f(x) = x 3 + 4 Leading Term: __________ Leading Coef : ______________ Degree : __________ x 3 1 → positive Odd

8. The Leading coefficient test

9. The Leading Coefficient Test This test can help you determine the end behavior of the graph of polynomial functions by looking at the degree and the leading coefficient so that it will give you a rough sketch of the graph.

10. End behavior End behavior is a description of the values of the function as x approaches positive infinity or negative infinity.

11. End behavior

12. Example: P (x )= 2x 4 – 3x 3 + x -1 P (x )= -3x 2 – 6x + 4 P(x )= x 4 – 2x 3 – x 5 + 1 P(x)= x(x + 3)(1 + 2x)

13. Directions: Identify whether the graph of the following function has an odd or even degree and a positive or negativ e leading coefficient.

14. Try me  P(x) = -x 4 + 10x 2 – 9 y = + x 2 – 2x 3 + 18x – 9 f(x) = 4x 5 – 4x 2 – 19x +10 P(x) = –10x 2 + 9 + 3x 4

15. Directions: Identify whether the graph of the following function has an odd or even degree and a positive or negative leading coefficient.

16. Answer me: 1. P(x) = -4x 4 – 3x 3 + x 2 +4 y = 3x 2 + 6x 3 – 10 f(x) = (2x + 1)(-x – 3)(3x + 2)