Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Alg 2B Test Review Polynomials and Rational Functions Factor the polynomial to find the zeros and write the factored form. Describe the end behavior of the function. Without a calculator, sketch the graph. 1.) P(x) = 3x3-6x 3.) P(x) = x5-9x3 + 20x2 Graph the polynomial and determine how many local maxima and minima it has. 4.) y = 2x4-36 5.) y = x3-9x Find the quotient and remainder using long division. 6.) 6x3+2x2+22x+9 2x+5 Find all the real zeros and the factored form of the polynomial. Use the quadratic formula if necessary. 10.) P(x) = 2x3+x2-13X+6 11.) P(X) = X4-5X3-5X2+ 23X + 10 13. Give examples of polynomials with the following properties or explain why it is impossible to have a polynomial with the properties: a) a polynomial of degree 3 with no real zeros b) a polynomial of degree 4 with no real zeros c) a polynomial of degree 3 with 3 real zeros, only 1 of which is rational d) a polynomial of degree 4 that has 4 real zeros, none of which is rational 14. Given the graph of f(x), write a possible factorization for the equation of the function. 15. Using proper notation, describe the end behavior for f(x) = -3x5+ 5x + 2 16. Write a polynomial function with degree 5 that has three real zeros at x = 4, x = -2, and x = √3. Analyze the following rational functions. Find domain, x and y intercepts, find equations of asymptotes and describe with limit notation 16. y = (3x-2)/(5x-10) 17. Y = (x-2)/(x2 – 4) 18. y = 4/(x2 + 1) 19. Y = 3x/(x2 + x) 20. What is a discontinuity in a function? Name the two types of discontinuities and how you can determine them algebraically and identify them graphically. Simplify the following expressions. 21. [3x5/(x2 – 2x) ]* [(x2 – 4)/9x] 22. (2x2 + 5x + 2)/(2x2 – 18) divided by (x2 + 7x + 10)/(5x + 15) 23. 2/(x+4)2 - 5/(x2 – 16) 24. 3/5x + 4x/15x2 Solve 25. 3/(x-5) + 2 = 4/(x+2)