Review and Supplemental Review Unit 2b: Polynomial and Rational Functions
Review and Supplemental Review 2.1: Quadratics, Parabolas, Standard Form Unit 2b: Polynomial and Rational Functions 1. The graph of is shifted 1 units to the right and 1 units down. What is the equation of the new graph written in standard form? 2. Write in standard form. Identify the vertex, axis of symmetry, and zeros. In terms of SRT transformations, how does the graph of the function in Q2 differ from its parent function? 4. Write a quadratic function whose graph passes through (−2, −8) and whose vertex is at (−4, −6). 5. Identify the vertex of 2.2: Polynomial Functions, End Behavior, Multiplicity 7. Describe the degree and leading coefficient of the polynomial function graphed below. 8. Bookwork: P. 208: 19 3. 6. Write a function whose graph has the following end behavior: As , As , . Without graphing the function, describe the end behavior of As As y x 9. The graph of a polynomial function of degree 5 is tangent to the -axis at (0, 0) and crosses the -axis at (−4, 0). If those are the only zeros of the function, and the graph passes through the point (−2, 6), what is the equation of the function? 10. Let a) How many zeros does . have? b) How many distinct zeros does c) have? Describe the behavior of the graph at . d) Describe the behavior of the graph at . e) . Describe the behavior of the graph at , , _____ _____ 2.3: Polynomial Division 11. Use synthetic division to divide [ ] into 12. What conclusion can you draw about Q11 based on the remainder? 13. Find the value of k such that the divides evenly into . 2.4: Complex Numbers 14. Write in standard form: 15. Perform the operation and write in standard form: 16. Find the value of : 17. Expand 2.5: Zeros of Polynomials Bookwork: P. 209: 49 P. 209: 54 18. Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and has 2, , and as zeros. 19. Explain why a polynomial of odd degree must have at least one rational zero. 21. Use the table below to help you find the zeros of the function. Then graph the function. -3 -2 -1 0 1 2 3 -50 21 12 -5 42 225 616 Bookwork: P. 210: 83-88 (86, 88) P. 210: 89 P. 210: 91-96 (92, 96) P. 210: 99-102 (100) P. 210: 103-106 (104, 106) P. 210: 108 20. Let be a polynomial such that and . Explain why must have a zero between and . 22. Find all the zeros of the function and then graph it. 2.6: Rational Functions 23. Bookwork: P. 210: 113, 114 For Q23-Q29, sketch the graph of each rational function without the aid of a graphing utility. But first a) find the vertical asymptotes, b) find the horizontal/slant asymptote, c) find the and -intercepts, and then finally d) graph the thing. 24. 26. 25. 27. 28. 29. 30. 4 the dashed graph. Graph ( ) 2 5 2 4 is the solid graph and is .