Rovew Test 3 MATHER SHORT ANSWER. Write the ward or phrase that best completes each statement or answers the question. List the possible rational zeros. 50 1 1 = 25 Factor 2 25 21 8 + 29 + 5, 1 1 fact , + 25, I's Find all the rational zeros. 2) f(x) =x4- 6x -5x2- 12x- 14 2) A polynomial f(x) and one of its zeros are given. Find all the zeros. 3) f(x) = x* - 6x3 + &2+30x- 65; 3 - 2i is a zero Determine the number of possible positive and negative real zeros for the given function. 4) f(x) =-8x- 7x4 - 683 + 4x2+ 6.x + 5 5 ) f ( x ) = 2x7 + 7x4 + 413 + 912-5x - 1 Solve the problem. 6) Determine if the upper bound theorem identifies 4 as an upper bound for the real 6 ) zeros off (x). f (x) = 8x' - & + 3x-9 Write the domain in interval notation. 7 ) f ( x ) = * - 81 x+ 9 7)Refer to the graph of the function and complete the statements. 8 ) Asx - -0of(x ) - 8 ) As x -+ 0of(x)- . . -15 :-10 . . 15. Determine the vertical asymptote(s) of the graph of the function. x +9 9 ) f (x ) = - 9) 7x2 + 9x - 10 a + 4 10) f(a) = 10) a + 30 - 5 a. Identify the horizontal asymptote (if any). b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. 11 ) f ( x ) = 2x2 + 2x - 5 11) x 2 + 2 Solve the problem. 12) The graph of f(x ) = 10x 3+ 8 13x 3 will behave like which function for large values of 12) /x / ?Graph the function by using a transformation of the graph of y = 1. 13) f (x) = - 13) * + 2 The graph of y = f(x) is given. Solve the inequality. 14 ) f ( x ) So 14) Solve the inequality. Write the solution set in interval notation. 15 ) - 15) x - 2 9- X 16) - 16) 'x+ 11 - 20 A relation in x and y is given. Determine if the relation defines y as a one-to-one function of x. 17) { ( -6, 8), -5, -8), (4, -6), (1, 3) ; 17)Determine if the relation defines y as a one-to-one function of x. 18) 18) Use the definition of a one-to-one function to determine if the function is one-to-one. 19 ) f (x ) =-2x2-13 19) 20) f (x ) = /x - 41 20) Determine whether the two functions are inverses. 21) f (x) = 6x + 6 and g (x) =- 6+x 21) A one-to-one function is given. Write an expression for the inverse function. 22 ) f ( xx ) = Vox + 7 22 23 ) f (x ) = - 6 - x 23) 2 24) f (x ) = *+8 24) x + 6 Solve the problem. 25) Given that the domain of a one-to-one function f is [-8, -1) and the range of fis ( 25) 8, 00), state the domain and range of f" Graph the function and write the domain and range in interval notation. 26) f (x) = 5* 26)27) 5()-5 27) Simplify the expression. 28) log , 16 Simplify the expression without using a calculator. 29) log 10,000,000,000 30) log, V2 Simplify the expression. log (25 - 7) 31) 4 Graph the function. 32) y = log,x 32) Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. 33) Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. 34) 51ogb y + 31ogb = 34) Solve the problem. 35) Use logb 3 ~ 0.319, use the properties of logarithms to approximate the 35) following. Do not use a calculator. log 81 Solve the equation. 36) 32 *+5 = 43x - 1 36) Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4 decimal places if necessary. 37) log s(6x - 14) = 1 + log 5(x - 2) 37) 38) In x + In(x + 4) = In(2x + 35) 38)Solve the equation. 39) 49148 - 74x 39) Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. 40) 310g5 m - 81085 n 40) Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. 41) 1086 x4yS 41) Write the equation in exponential form. 12) log 4 16 = 2 42) Determine whether the two functions are inverses. 43 ) f ( x ) = - 2 2 + 3x 2 and g (x) =- 43) *+ 3 Classify the matrix as a square matrix, row matrix, column matrix, or none of these. 44) Find A + B. 45) Perform the indicated operations. 46) Find -54 - 4B. 46) 1 -1 2 8 9 ) and B - [ # 3 : ]Given the matrices A and B, solve for X. 47) 5X - B = A. 47) 1=3 8 and B = [ 3 3] Find AB, if possible. 2 by 3 = ) 3672 48 ) A = 7 5 8 and B - 3 8 3 51 2 2+3 32 48 Evaluate the determinant of the given matrix. 49) A = -7 9 49) 50 ) A = 3 4 50)