Math 1314 - College Algebra Instructor: Dalip Sondhi Exam 3 N ame__________________________________ D ate________________________ PLE ASE SUBMIT T H IS TEST, SU M M ARIZ E Y O UR A NSWERS O N IT, ST APLE YO UR SUPPORTI N G W SC A N TRO N INSERTED BE H IN D PA GE 1, U NST APLED. GRA DI N G RUBRIC: 40% F OR C ORRECT A NSW ERS, 50% FOR C O MPLETE & C ORRECT SUPPORTIN G W N E A T & PRO FESSIO N A L W ORK. D U E D A TE: D ECEMBER 1, 2016 TuTh , D ECE MBER 4, 2016 Sun MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the quest Determine whether the function is a polynomial function. If so, determine the degree. x2 - 3 1)f(x) = x6 A) polynomial function; degree 2 C) polynomial function; degree 3 1) D B)polynomial function; degree 6 D) not a polynomial function Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial func this end behavior to match the polynomial function with its graph. 2 + 2x - 2 4x - 3x 2) 2)f(x) = - 3 A) B) D C) D) 1 Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 4 - 2x 3 + 5x 2 + 3x + 4 3) 3)f(x) = 3x A) falls to the left and rises to the right B)falls to the left and falls to the right C) rises to the left and rises to the right D) rises to the left and falls to the right C Find the zeros of the polynomial function. 2- x - 6 4)f(x) =3x+ 6x A) x = 36 C) x = - 1, x = 1, x = - 6 C 4) B)x = - 6, x = 6 D) x = 1, x = - 6, x = 6 Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the grap x-axis or touches the -axis x at each zero. 12 3 5) 5)f(x) = (x +) (x - 6) 5 1 A) x = - has multiplicity 2; The graph touches the x- axis and turns around; x = 6 has 5 multiplicity 3; The graph crosses the x -axis. 1 B)x = has multiplicity 2; The graph touches the x- axis and turns around; x = -6 has 5 multiplicity 3; The graph crosses the x -axis. 1 C) x = - has multiplicity 2; The graph crosses the x- axis; x = 6 has multiplicity 3; The graph 5 touches the x and turns around. -axis 1 D)x = has multiplicity 2; The graph crosses the x- axis; x = - 6 has multiplicity 3; The graph 5 touches the x and turns around. -axis Divide using synthetic division. 2 + 29x- 30 5x3 - 34x 6) x- 6 2 - 6x - 5 A) - 5x B)5x2 - 4x + 5 5 17 29 x+ C) x2 6 3 6 2 + 6x + 5 D)- 5x Solve the problem. 3 + 4x 2 - 4x + 16, use the Remainder Theorem to find f(2). + 9x 7) Given f(x) =47x A) f(2) = 304 B)f(2) = 208 C) f(2) = 40 D)f(2) = 16 3 - 3x 2 + 51x - 14 = 0 given that 2 isf(x) 3of 2 + 51x - 14. 28x a zero = 3x - 28x 8)Solve the equation 1 7 7 1 A) {2, - 7, -} B){2, - 1, -} C) {2, 1,} D){2, 7,} 3 3 3 3 2 6) B 7) B 8) D Use the Rational Zero Theorem to list all possible rational zeros for the given function. 3 - x2 + 3 9) 9)f(x) = 5x 1 3 1 5 A) , , 1, 3 B) , , 1, 5 5 5 3 3 1 1 C) , , 1, 3, 5 5 3 1 3 D) , , 1, 3, 5 5 5 Find a rational zero of the polynomial function and use it to find all the zeros of the function. 3 - 17x 2 + 18x + 8 10) 10)f(x) = 3x 1 4 1 4 A) , 2, - 4 B) - , - 1, - 2 C) - , 2, 4 D) , - 1, 2 3 3 3 3 List all possible rational roots, use synthetic division to find an actual root, then use this root to solve th 2 + 12x - 18 = 0 11) 11)x3 + 5x A) { 1, - 3 + 3i, - 3 - 3i} B){ 1, 3 +5, 3 - 5} 5, - 6 - 5} C) {- 1, - 3 + D) { 1, 3 + 3i, 3 - 3i} Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for th 5 - 5x4 + x + 7 12) 12)f(x) = 6x A) 2 or 0 positive zeros, 1 negative zero B)2 or 0 positive zeros, 2 or 0 negative zeros C) 2 or 0 positive zeros, 1 or 0 negative zeros D)3 or 1 positive zeros, 3 or 1 negative zeros Use the Upper and Lower Bound Theorem to determine integer-valued bounds to the real zeros of the po function. 3 - 7x 2 - 5x + 10 13) 13)f(x) =4x+ x A) -1 and 1 B) -4 and 3 C) 0 and 5 D) -2 and 4 Use the Intermediate Value Theorem to show that the polynomial has a real zero between the given integ 4 - 6x 2 - 5; between 1 and 2 14) 14)f(x) = 3x A) f(1) = - 7; f(2) = 20 B)f(1) = - 8; f(2) = 19 C) f(1) = 8; f(2) = 19 D) f(1) = 8; f(2) = - 19 Find the domain of the rational function. 6x2 15)h(x) = (x + 1)(x - 8) 15) A) {x | x-1, x 8, x - 6} C) all real numbers B){x | x 1, x - 8} D) {x | x-1, x 8} Find the vertical asymptotes, if any, of the graph of the rational function. x- 4 16)f(x) = x(x+ 1) A) x = 4, x = - 1 C) x = 0, x = - 1 B)x = - 1 D) no vertical asymptotes 3 16) Find the horizontal asymptote, if any, of the graph of the rational function. - 2x + 7 17)f(x) = 4x- 3 1 A) y = 2 B)y = - 2 7 C) y = 3 D) no horizontal asymptote Graph the rational function. 3x 18)f(x) = (x- 5)(x+ 5) 17) 18) A) B) C) D) Find the slant asymptote, if any, of the graph of the rational function. x2 + 6x- 5 19)f(x) = x- 6 A) x = y + 12 C) y = x - 0 B)y = x + 12 D) no slant asymptote 4 19)