Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

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1 Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D) x -3; {3} Add or subtract as indicated and write the result in standard form. 2) -3 - (- 4-3i) - ( i) 2) A) 6 + 2i B) 9-2i C) 9 + 2i D) 6-2i Divide and express the result in standard form. 5i 3) 4-5i A) i B) i C) i D) i 3) Solve the equation by factoring. 4) x2 = x ) A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} Solve the equation using the quadratic formula. 5) 7x2-9x + 3 = 0 5) A) -9 ± 3 14 B) 9 ± i 3 14 C) -9 ± i 3 14 D) 9 ± 3 14 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 + 1) ) A) (-6, 2) B) [-6, 2] C) [-8, 0] D) (-8, 0) Determine whether the relation is a function. 7) {(-8, -5), (-8, -7), (2, 7), (6, -1), (8, 5)} 7) A) Not a function B) Function 1

2 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) function B) not a function 9) 9) A) not a function B) function Use the graph to determine the function's domain and range. 10) 10) A) domain: [0, ) range: (-, ) B) domain: [0, ) range: [0, ) C) domain: (-, ) range: [-1, ) D) domain: [0, ) range: [-1, ) 2

3 Use the given conditions to write an equation for the line in slope-intercept form. 11) Slope = 2, passing through (5, 2) 11) 3 A) y = mx B) y = 2 3 x C) y = 2 3 x D) y = 2 3 x ) Passing through (4, 4) and (2, 7) 12) A) y - 4 = (x - 4) B) y = 3 2 x + 10 C) y = mx + 10 D) y = x + 10 Graph the equation in the rectangular coordinate system. 13) x = -3 13) A) B) 3

4 C) D) 14) y = 4 14) A) B) 4

5 C) D) Graph the equation. 15) 4x + 5y - 18 = 0 15) A) B) 5

6 C) D) Find an equation for the line with the given properties. 16) The solid line L contains the point (4, 1) and is perpendicular to the dotted line whose equation is 16) y = 2x. Give the equation of line L in slope-intercept form. A) y - 1 = (x - 4) B) y = 1 2 x + 3 C) y - 1 = 2(x - 4) D) y = x + 3 6

7 17) The solid line L contains the point (3, 2) and is parallel to the dotted line whose equation is y = 2x. 17) Give the equation for the line L in slope-intercept form. A) y = 2x - 1 B) y - 2 = 2(x - 3) C) y = 2x - 4 D) y = 2x + b The graph of a quadratic function is given. Determine the function's equation. 18) 18) A) g(x) = -x2 + 6x + 9 B) h(x) = -x2-3 C) f(x) = -x2-6x - 9 D) j(x) = -x2 + 3 Find the coordinates of the vertex for the parabola defined by the given quadratic function. 19) f(x) = (x + 1)2-5 19) A) (1, 5) B) (-1, 5) C) (-1, -5) D) (1, -5) Use the vertex and intercepts to sketch the graph of the quadratic function. 7

8 20) y + 4 = (x - 1)2 20) A) B) C) D) Divide using synthetic division. 21) (5x5 +12x4 + -5x3 + x2 - x + 105) (x + 3) 21) A) 5x4-3x3 + 4x2-12x x + 3 C) 5x4-3x3 + 4x2-11x x + 3 B) 5x4-3x3 + 4x2-12x x + 3 D) 5x4-3x3 + 4x2-11x x + 3 8

9 Use synthetic division and the Remainder Theorem to find the indicated function value. 22) f(x) = x5 + 3x4 + 3x3-4; f(-3) 22) A) -13 B) 158 C) 85 D) -85 Use the Rational Zero Theorem to list all possible rational zeros for the given function. 23) f(x) = -2x3 + 2x2-4x ) A) ± 1 8, ± 1 4, ± 1 2, ± 1, ± 2, ± 4, ± 8 B) ± 1 4, ± 1, ± 1, ± 2, ± 4, ± 8 2 C) ± 1 2, ± 1, ± 2, ± 4 D) ± 1, ± 1, ± 2, ± 4, ± 8 2 Find the domain of the rational function. 8x2 24) h(x) = (x - 3)(x + 5) 24) A) {x x 3, x -5} B) {x x -3, x 5} C) all real numbers D) {x x 3, x -5, x -8} Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 25) 3x2 + 11x ) A) (-, -5] 4, B) [-5, ) 3 C) -, 4 3 D) -5, 4 3 Write the equation in its equivalent logarithmic form. 26) 2-3 = ) A) log = 2 B) log 1/2 2 = -3 C) log 2-3 = 1 8 D) log = -3 27) = 6 27) A) log = 1 3 B) log = 3 C) log = 1 6 D) log = 1 3 9

10 Evaluate the expression without using a calculator. 28) log ) A) 10 B) 2 C) 20 D) 100 Evaluate or simplify the expression without using a calculator. 29) 5 10 log ) A) 360 B) 3.6 C) 36 D) ) ln e10 30) 1 A) e B) 10 C) D) 1 10 Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. x2 31) log 31) 5 y6 A) 6 log 5 y - 2 log 5 x B) 2 log 5 x + 6 log 5 y C) 1 3 log 5 (x y ) D) 2 log 5 x - 6 log 5 y Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 32) 1 3 (log 6 x + log6 y) - 5 log6 (x + 4) 32) A) log6 3 x + y (x + 4)5 B) log6 3 xy 5(x + 4) C) log6 3 x + 3 y (x + 4)5 D) log6 3 xy (x + 4)5 Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 33) log ) 17 A) B) C) D) Solve the equation by expressing each side as a power of the same base and then equating exponents. 34) 4(1 + 2x) = ) A) {2} B) {-2} C) {8} D) {256} 35) 64x = 16 35) A) 4 B) 3 2 C) 2 3 D)

11 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 + 1) + log (x - 5) = 3 36) 3 3 A) {9} B) {-4} C) {8, -4} D) {8} Determine whether the given ordered pair is a solution of the system. 37) (5, -3) 37) x + y = 2 x - y = 8 A) not a solution B) solution Solve the system of equations by the substitution method. 38) 38) x + y = -3 y = -2x A) {(-3, 6)} B) {(3, -6)} C) {(3, 6)} D) {(-3, -6)} Solve the system by the addition method. 39) -4x + y = 3 39) -2x + 5y = 6 A) 5, 4 1 B) {(1, -1)} C) 5 2, 5 D) - 1 2, 1 Graph the solution set of the system of inequalities or indicate that the system has no solution. 40) 3x - y 9 40) x + 4y 4 11

12 A) B) C) D) Give the order of the matrix, and identify the given element of the matrix. 41) 41) e ; a A) 5 4; 12 B) 4 5; -12 C) 4 4; -3 D) 20; 9 Solve the matrix equation for X. 42) 42) Let A = 0-2 and B = 1 2 ; B - X = 3A A) X = B) X = C) X = D) X =

13 Find the product AB, if possible. 43) 43) A = , B = A) B) AB is not defined. C) D)