4.5 Notes

1. 4.5 Notes Graphing polynomial functions

2. 4.5 Notes parts of the graph of a polynomial function

3. 4.5 Notes In this course, you will graph polynomial functions by… Plotting the exact number (and sometimes the exact value) of real roots. Plotting the y-intercept. Sketching a curve that has right-end behavior corresponding to the function’s leading coefficient. Sketching a curve with a number of direction changes corresponding to one less than the function’s degree.

4. 4.5 Notes In this course, you will sketch a graph with the approximate location of absolute and relative maximums and minimums for a function. In later course(s), you may also learn to graph polynomial functions by plotting the exact value of the coordinates of absolute and relative maximums and minimums.

5. 4.5 Notes If you are provided a polynomial function that is in factored form, sketch a curve that intersects the x-axis at the exact values of the zeros of the function.

6. 4.5 Notes Determine the roots of the equation given the factors of the equation. 1. 2. 3. 4.

9. 4.5 Notes If you are provided a polynomial function that is not in factored form, use the Upper and Lower Bound Theorems and the Location Principle to sketch a curve that intersects the x-axis at the approximate values of the zeros of the function.

10. 4.5 Notes LUB: 3 GLB: -2

12. 4.5 Notes LUB: 2 GLB: -3 A root lies between -3 and -2.

14. 4.5 Notes LUB: 3 GLB: -1 This polynomial has no real roots.

16. 4.5 Notes Practice problems: 1. 2.