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1 Student: Date: Instructor: kumnit nong Course: MATH 105 by Nong Assignment: CH test review 1 Find the transformation form of the quadratic function graphed in the figure to the right 10 8 p(x) p(x) = 6 4 x Find the end behavior of the following polynomial function 5 3 g(t) = 14t + 56t + 405t + 395t As t, g(t), and as t, g(t) 3 Multiply the polynomial functions f(x) = 3x + 4x and g(x) = 3x (fg)(x) = (Simplify your answer Do not factor) 4 f(x) Divide f(x) by g(x) given below, and write the answer in the form quotient g(x) = + remainder divisor 3 f(x) = 15x 6x + 16x + 4; g(x) = 5 x x 3 6x + 16x + 4 = 5x of 8 9/1/18, 7:05 PM

2 5 a Use long division to simplify f(x) = 5x3 x x + 1 b Describe the behavior of f as x grows large and positive c Describe the behavior of f as x grows large in magnitude and negative d What is the range of f? e Let f(x) = p(x) Describe the end behavior of f if p is a polynomial of even degree and d is a polynomial of odd degree d(x) a 5x3 x x = + 1 (Simplify your answer) b As x, f(x) c As x, f(x) d The range of f(x) is (Type your answer in interval notation) e Choose the correct answer below A The remainder r will be an even-degree polynomial, so the end behavior will be like that of an even-degree polynomial regardless of the behavior of the divisor B The quotient q will be an odd-degree polynomial, so the end behavior will be like that of an odd-degree polynomial C The quotient q will be an even-degree polynomial, so the end behavior will be like that of an even-degree polynomial D The remainder r will be an odd-degree polynomial, so the end behavior will be like that of an odd-degree polynomial regardless of the behavior of the divisor 6 a Find the factored form of a polynomial function f whose roots are given as below Use a as the leading coefficient b Find values of the leading coefficient for which the coefficients of f in standard form are integers Roots: 3 5, 3 5,5, 14 3 a The factored form of a polynomial function is f(x) = b Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The value of the leading coefficient is B The value of the leading coefficient is any positive real number C The value of the leading coefficient is any negative real number D The values of the leading coefficient are the integer multiples of of 8 9/1/18, 7:05 PM

3 7 Find the root, factored, and standard forms of a polynomial function f whose only roots are the given rational roots Roots: 9 7, 5 ; f(0) = 54 The root form of a polynomial function is f(x) = (Simplify your answer Use integers or fractions for any numbers in the equation) The factored form of a polynomial function is f(x) = (Simplify your answer) The standard form of a polynomial function is f(x) = (Simplify your answer) 8 Write a polynomial p with the given properties A polynomial p is a third-degree polynomial whose graph passes through the points ( 3,0), (0,0), (,0), and ( 1, 8) p(x) = (Type an expression using x as the variable Simplify your answer) 9 p The Rational Root Theorem states that if a simplified rational number is a root of the polynomial q n n 1 f(x) = anx + an 1x + + a1x + a0, whose coefficients are integers, then p must be a factor of the constant term a 0 and q must be a factor of the leading coefficient a n Use the theorem to create a list of all rational numbers that could be 3 roots of the polynomial function f(x) = x 6x 16x + 49 Choose the complete list of all rational numbers that could be roots of the polynomial function { ± 1, ± 49} { ± 1, ± 7, ± 49} { ± 1, ± 7} { ± 7} 10 Find a polynomial p with the following properties having the smallest possible degree p has a root i with multiplicity The polynomial p is (Type an expression using x as the variable Do not factor) 3 of 8 9/1/18, 7:05 PM

4 11 Find any x-intercepts, vertical asymptotes, and holes for the graph of the following function f(x) = 3x x What is/are the x-intercept(s) of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The x-intercept(s) of the function is/are (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) B The function has no x-intercept What is/are the vertical asymptote(s) of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The function has two vertical asymptotes The leftmost asymptote is The rightmost asymptote is (Use integers or fractions for any numbers in the equations) B The function has one vertical asymptote, (Use integers or fractions for any numbers in the equation) C The function has no vertical asymptotes At which point(s) does the given function have hole(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The function has hole(s) at (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) B The function has no holes 4 of 8 9/1/18, 7:05 PM

5 1 Find any x-intercepts, vertical asymptotes, and holes for the graph of the following function (x 1) (x + 3) f(x) = (x 1)(3x 8)(x + 3) What is/are the x-intercept(s) of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The x-intercept(s) of the function is/are (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) B The function has no x-intercepts What is/are the vertical asymptote(s) of the given function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The function has two vertical asymptotes The leftmost asymptote is The rightmost asymptote is (Use integers or fractions for any numbers in the equation) B The function has one vertical asymptote, (Use integers or fractions for any numbers in the equation) C The function has no vertical asymptotes At which point(s) does the given function have hole(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The function has hole(s) at the point(s) (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) B The function has no holes 13 Write a rational function f with the following properties f has vertical asymptote x =, hole at x = 1, x-intercept ( 7,0), and end behavior model q(x) = 3 f(x) = 14 Write the inequality 3x 6 9 without an absolute value (Do not simplify Type a compound inequality) 15 x + Suppose Write an inequality satisfied by x when x Write an inequality satisfied by x when x x 5 < 6 > 5 < 5 Write an inequality satisfied by x when x > 5 (Type an inequality) Write an inequality satisfied by x when x < 5 (Type an inequality) 5 of 8 9/1/18, 7:05 PM

6 16 Solve the following absolute value inequality 1 6 4x < 6 The solution set is (Type your answer in interval notation Simplify your answer) 17 Solve the following polynomial inequality 10x 1 9x The solution set is (Type your answer in interval notation Simplify your answer Type an exact answer, using radicals as needed) 18 Solve the following polynomial inequality using a sign chart 4x + 1 5x Select the correct choice below and, if necessary, fill in the answer box to complete your choice A The solution set is (Type your answer in interval notation Simplify your answer) B There is no solution 6 of 8 9/1/18, 7:05 PM

7 1 (x 3) x 1x + 1x + 8x x 3x x x 5x + x + 1 (, ) B The quotient q will be an odd-degree polynomial, so the end behavior will be like that of an odd-degree polynomial a 6 (5x 3)(5x 3)(x 5)(3x 14) 75 D The values of the leading coefficient are the integer multiples of x x 7 3(7x 9)(5x ) 105x 177x x x + 1x 9 { ± 1, ± 7, ± 49} x + 1x + 86x + 300x of 8 9/1/18, 7:05 PM

8 11 A The x-intercept(s) of the function is/are 4,0 3 (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) B The function has one vertical asymptote, x = 9 (Use integers or fractions for any numbers in the equation) 8 B The function has no holes 1 A The x-intercept(s) of the function is/are 3,0 (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) A The function has two vertical asymptotes The leftmost asymptote is x = 3 The rightmost asymptote is x = 8 3 (Use integers or fractions for any numbers in the equation) A The function has hole(s) at the point(s) (1,0) (Simplify your answer Type an ordered pair, using integers or fractions Use a comma to separate answers as needed) 13 3(x 1)(x + 7) (x 1)(x + ) x x + < 6(x 5) x + > 6(x 5) 16, , 17, 3 5 7, 18 A The solution set is 3 4,7 (Type your answer in interval notation Simplify your answer) 8 of 8 9/1/18, 7:05 PM