MATH 121 Final: MATH 121 Amherst S18M121 2801 29PfluegerFinal

Graph the polynomial function. a) Describe end behavior. bi Find all zeros and indicate if it crosses or touches and turns at each zero. Find the y-intercept, if applicable, to help graph the function 14) f(x)--r+4 10 1034 10 10 요 10 10 Divide using long division. Divide using synthetic division. 20x-26x -7x+19 175-4 18) x- 2 Use synthetic division and the Remainder Theorem to find the indicated function value. 19) s(x)+8+8+5x-4/(-4) Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.

Name: Algebra II Honors Chapter 4 TEST Review er. Determine whether the given quadratic functions have a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. (x)--2x' +8 Solve the problem. The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)--40x+144. Find the number of automobiles that must be produced to minimize the cost. 3) Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Find the zeros of the polynomial function. 7) f(x) +x'-20 Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosse the x-axis or touches the x-axis and turns around, at each zero. o) x)-sr(-5)(x+s) Determine the maximum possible number of turning points for the graph of the function. 2 f(x)- +8x 13) f(x)x+1

183 .1 GRAPHS OF POLYNOMIALS 3.1.1 EXERCISES n Bxeacises 1-10, find the degre, the leading term, the leading coefficient, the constant term and the end behavlor of ng to a 5 8. Qua ettinged nds to be 10. G(t) = 4(1-2)2(1+1) In Exercises 1 1·20, find the real zeros of the given polymotnial and their corresponding multiplicities. Use this information long with a sign chart to provide a rough sketch of the graph of the polynomial. Compare your answer with the result from agraphing utility the gra at 1-1 12. g(x)=x(x +2)3 14. g)(2x+1)P Cx-3) 16, p(x)=(x-1)(x-20x-3)(x-4) 18. h(x)=x2(x-2)2(x+2)2 11, a(x)=x(x +2)2 19. hrs-a-r)(r2 + 1) (x) by starting with the graph of y- transformations. State the domain and In Exercises 21-26, given the pair of functions f and g, sketch the graph of y = and using transformations. Track at least three points of your choice through the range of g. 21. f(x)=r', g(x) =(x+2)3 +1 23. f(x)ar', g(x)#2-3(x-1)4 25. f(x)-r, g(x) (x+1)s + 10 27, Use the Intermedlate Value Theorem to prove that fu)9x+5hs 22. f(x) =xt,gtx)=(x+2)4+1 26, f(x)=e,g(x)=8-2 has a real zero in each of the follonding intervale 1-4,-3),10,1] and [2,3). 28. Rework Example 3.1.3 assuming the box is to be made from an 8.5 inch by II lnch shet of papet.Using scisorm CD TVs isgven

Complete the sentence below. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. Complete the sentence below. The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and If r is a solution to the equation f(x) = 05 name three additional statements that can be made about f and r assuming f is a polynomial function. Choose the correct answer below. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is an x-intercept of the graph of and x - r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a complex zero of the polynomial function r is an x-intercept of the graph of and x + r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is a y-intercept of the graph of x and x + r is a factor of f. Explain what the notation Km f(x) = -infinity means. x rightarrow infinity Choose the correct answer below. The limit of f(x) as x approaches - infinity equals infinity. The limit of x as f(x) approaches infinity equals - infinity. The limit of f(x) as x approaches infinity equals - infinity. The limit of x as f(x) approaches - infinity equals infinity. Form a polynomial whose zeros and degree are given. Zeros: -7, multiplicity 1; - 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. F(x) = Find the vertical horizontal and oblique asymptotes, if any, for the following rational function.R(x) = 12x / x + 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 64 / x2 - 6x + 8 Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, for the given rational function. Q(x) = 2x2 - 7x - 4 / 3x2 - 7x - 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) There is no vertical asymptote. Analyze the graph of the function. R(x) = x + 14 / x(x + 15) What is the domain of R(x)? {x x 0 andx - 16} {x x 0 andx - 16 andx - 14} {x x 0 and x - 14} All real numbers Analyze the graph of the function. R(x) = 5x + 5 / 4x + 12 What is the domain of R(x)? {x|x 0 and x -3 and x - 1} {x|x -3} {x|x and x - 3} All real numbers Analyze the graph of the function.R(x) = x2 / x2 + x - 56 What is the domain of R(x)? {x|x 7 and x - 8} {x|x 0,x -1, and x 8} {x|x 0, x 7, and x - 8} All real numbers