Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add or subtract as indicated and write the result in standard form. 2) -7 - (5-5i) - (- 6-5i) 2) A) -6-0i B) -6 + 0i C) + 0i D) - 0i Divide and express the result in standard form. 3i 3) 7 + 2i A) 2 53 + 6 53 i B) 6 53 + 2 53 i C) 7 5 + 2 5 i D) 2 5-7 5 i 3) Solve the equation by factoring. 4) x2 = x + 72 4) A) {, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} Solve the equation using the quadratic formula. 5) 8x2-9x + 6 = 0 5) A) 9 ± 6 B) -9 ± i 6 C) 9 ± i 6 D) -9 ± 6 Solve the absolute value inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 6) 3(x + ) + 9 2 6) A) [-6, 2] B) (-6, 2) C) [-8, 0] D) (-8, 0) Determine whether the relation is a function. 7) {(-9, -6), (-9, -8), (, 6), (3, 5), (9, 6)} 7) A) Function B) Not a function
MAC 05 - College Algebra Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. 8) 8) A) not a function B) function 9) 9) A) not a function B) function Use the graph to determine the function's domain and range. 0) 0) A) domain: [0, ) range: [0, ) B) domain: (-, ) range: [3, ) C) domain: [0, ) range: [3, ) D) domain: [0, ) range: (-, ) 2
MAC 05 - College Algebra Use the given conditions to write an equation for the line in slope-intercept form. ) Slope = 8, passing through (8, 8) ) 9 A) y = 8 9 x + 8 9 B) y = 8 9 x + 8 C) y = 8 9 x - 8 9 D) y = mx + 8 9 2) Passing through (6, 7) and (7, 5) 2) A) y = 2x + 9 B) y - 7 = - 2(x - 6) C) y = - 2x + 9 D) y = mx + 9 Graph the equation in the rectangular coordinate system. 3) x = 5 3) A) B) 3
MAC 05 - College Algebra C) D) 4) y = 5 4) A) B) 4
MAC 05 - College Algebra C) D) Graph the equation. 5) 4x + 5y - 8 = 0 5) A) B) 5
MAC 05 - College Algebra C) D) Find an equation for the line with the given properties. 6) The solid line L contains the point (4, ) and is perpendicular to the dotted line whose equation is 6) y = 2x. Give the equation of line L in slope-intercept form. A) y = 2 x + 3 B) y = - 2 x + 3 C) y - = - (x - 4) D) y - = 2(x - 4) 2 6
MAC 05 - College Algebra 7) The solid line L contains the point (2, ) and is parallel to the dotted line whose equation is y = 2x. 7) Give the equation for the line L in slope-intercept form. A) y = 2x - B) y - = 2(x - 2) C) y = 2x + b D) y = 2x - 3 The graph of a quadratic function is given. Determine the function's equation. 8) 8) A) f(x) = -x2-4x - 4 B) h(x) = -x2-2 C) j(x) = -x2 + 2 D) g(x) = -x2 + 4x + 4 Find the coordinates of the vertex for the parabola defined by the given quadratic function. 9) f(x) = (x + 4)2-9) A) (-4, -) B) (4, -) C) (4, ) D) (-4, ) Use the vertex and intercepts to sketch the graph of the quadratic function. 7
MAC 05 - College Algebra 20) y - 6 = (x + 2)2 20) A) B) C) D) Divide using synthetic division. 2) (3x5 +4x4 + -0x3 + x2 - x + 24) (x + 3) 2) 5 5 A) 3x4-5x3 + 5x2-5x + 42 + B) 3x4-5x3 + 5x2-5x - 42 + x + 3 x + 3 C) 3x4-5x3 + 5x2-4x + 4 + x + 3 D) 3x4-5x3 + 5x2-4x - 42 + x + 3 8
MAC 05 - College Algebra Use synthetic division and the Remainder Theorem to find the indicated function value. 22) f(x) = x5-8x4-8x3 + 3; f(4) 22) A) -533 B) 533 C) -93 D) -2557 Use the Rational Zero Theorem to list all possible rational zeros for the given function. 23) f(x) = -2x3 + 2x2-3x + 8 23) A) ± 8, ± 4, ± 2, ±, ± 2, ± 4, ± 8 B) ±, ±, ± 2, ± 4 2 C) ± 2, ±, ± 2, ± 4, ± 8 D) ± 4, ±, ±, ± 2, ± 4, ± 8 2 Find the domain of the rational function. 2x2 24) g(x) = (x - 9)(x + ) 24) A) all real numbers B) {x x -9, x } C) {x x 9, x -} D) {x x 9, x -, x -2} Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 25) 2x2 + x - 6 0 25) A) [-6, ) B) -6, 2 C) -, 2 D) (-, -6] 2, Write the equation in its equivalent logarithmic form. 26) 2-3 = 8 26) A) log -3 8 = 2 B) log 2-3 = 8 C) log /2 2 = -3 D) log 2 8 = -3 27) 3 26 = 6 27) A) log 6 26 = 3 B) log 6 26 = 3 C) log 26 3 = 6 D) log 26 6 = 3 9
MAC 05 - College Algebra Evaluate the expression without using a calculator. 28) log 4 6 28) A) 4 B) 8 C) 6 D) 2 Evaluate or simplify the expression without using a calculator. 29) 6 0 log 7.7 29) A) 462 B) 4.62 C) 2.2473 D) 46.2 30) ln e0 30) A) e B) C) 0 D) 0 Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. x4 3) log 3) 2 y7 A) 4 7 log 2 (x y ) B) 4 log 2 x - 7 log 2 y C) 7 log 2 y - 4 log 2 x D) 4 log 2 x + 7 log 2 y Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is. Where possible, evaluate logarithmic expressions. 32) 6 (log 6 x + log6 y) - 4 log6 (x + ) 32) A) log6 6 x + y (x + )4 B) log6 6 xy 4(x + ) C) log6 6 xy (x + )4 D) log6 6 x + 6 y (x + )4 Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 33) log 60 33) 9 A) 0.79 B).3905 C) 3.0569 D) 0.4994 Solve the equation by expressing each side as a power of the same base and then equating exponents. 34) 3( + 2x) = 27 34) A) {-} B) {} C) {3} D) {9} 35) 325x = 25 35) A) 3 5 B) 3 C) 3 4 D) 5 3 0
MAC 05 - College Algebra Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 36) log (x - 5) + log (x - ) = 2 36) 4 4 A) {3, 3} B) {4} C) {3} D) {3} Determine whether the given ordered pair is a solution of the system. 37) (-4, 6) 37) x + y = 2 x - y = -0 A) solution B) not a solution Solve the system of equations by the substitution method. 38) 38) x + y = 9 y = -4x A) {(3, 2)} B) {(-3, -2)} C) {(3, -2)} D) {(-3, 2)} Solve the system by the addition method. 39) -3x + y = -7 39) 6x - 4y = 20 4 A) 3, -3 B) 7 3, 0 C) {(, )} D) -4, 4 Graph the solution set of the system of inequalities or indicate that the system has no solution. 40) 4x - y 4 40) x + 3y 9
MAC 05 - College Algebra A) B) C) D) Give the order of the matrix, and identify the given element of the matrix. 4) 4) -5-5 -0 5 5-3 -e -0 0 4 9 4 2 0 ; a34 8 0 7-9 3 A) 5 4; 0 B) 20; 0 C) 4 5; 2 D) 4 4; 4 Solve the matrix equation for X. 42) 42) -5 7-6 Let A = 0 2 and B = 5 ; B - X = 3A 7-9 0 6 A) X = 22-9 -5-5 -2 33 B) X = 22-9 5-5 -2 33 C) X = -8-3 -5 7 2-2 D) X = -8-3 -5 7 7-2 2
MAC 05 - College Algebra Find the product AB, if possible. 43) 43) A = 3-2 0 4-3, B = 5 0-2 2 A) C) 5-0 5-6 2-8 5 0 0 8 B) 5-6 -0 2 5-8 D) AB is not defined. 3