MAC 05 - College Algebra Name Review for Test 2 - Chapter 2 Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact distance between the points. ) (-4, -2) and (3, -) A) 0 B) 5 2 C) 0 D) 50 2) (8, -) and (2, 2) A) 0 B) 45 C) 0 D) 3 5 Find the midpoint of the line segment whose endpoints are the given points. 3) (2.8, -5.9) and (-5.4, 4.9) A) (4., -5.4) B) (-.55, -0.25) C) (-.3, -0.5) D) (-.3, -5.4) 4) (9.9, 4.7) and (-3.9, -7.5) A) (3, 6.) B) (6.9, 6.) C) (7.3, -5.7) D) (3, -.4) Find the x- and y-intercepts. 5) (x - 2)2 + (y + 3)2 4 = A) x-intercepts: (-, 0) and (, 0); y-intercepts: (0, -2) and (0, 2) B) x-intercept: (, 0); y-intercept: (0, 2) C) x-intercept: none; y-intercept: none D) x-intercept: (3, 0); y-intercept: (0, -) 6) x 2 + y = 36 Solve the problem. A) x-intercept: (0, 36); y-intercepts: (-6, 0) and (6, 0) B) x-intercepts: (-6, 0) and (6, 0); y-intercept: (0, 36) C) x-intercept: (6, 0); y-intercept: (0, 36) D) x-intercept: none; y-intercept: (0, 36) 7) Is the point (8, 2) on the circle defined by (x - 5) 2 + (y + 2) 2 = 25 A) No B) Yes Determine the center and radius of the circle. 8) (x - 7) 2 + (y - 8) 2 = 9 A) Center: (7, 8); Radius: 9 B) Center: (-7, -8); Radius: 3 C) Center: (7, 8); Radius: 3 D) Center: (-7, -8); Radius: 9
9) (x - 3) 2 + (y - 2) 2 = 54 A) Center: (3, 2); Radius: 3 6 B) Center: (-3, -2); Radius: 54 C) Center: (3, 2); Radius: 54 D) Center: (-3, -2); Radius: 3 6 Use the given information about a circle to find its equation. 0) center (2, 2) and radius 3 A) (x - 2) 2 + (y - 2) 2 = 3 B) (x + 2) 2 + (y + 2) 2 = 3 C) (x - 2) 2 + (y - 2) 2 = 3 D) (x + 2) 2 + (y + 2) 2 = 3 ) center (2, -5) and radius of 2 A) (x - 2) 2 + (y + 5) 2 = 2 B) (x + 2) 2 + (y - 5) 2 = 4 C) (x - 2) 2 + (y + 5) 2 = 4 D) (x + 2) 2 + (y - 5) 2 = 2 Use the given information about a circle to write an equation of the circle in standard form. 2) The endpoints of a diameter are (0, 6) and (-2, -0). A) (x + 0) 2 + (y + 6) 2 = 20 B) (x - 0) 2 + (y - 6) 2 = 00 C) (x - 4) 2 + (y + 2) 2 = 00 D) (x + 4) 2 + (y - 2) 2 = 20 Determine whether the relation defines y as a function of x. 3) A) Function B) Not a function 4) A) Function B) Not a function 2
5) A) Not a function B) Function Solve the problem. 6) Find f(2) for the given function. f (x) = -4 + x 2 A) -4 + 4x2 B) -8 C) 0 D) -8 + 2x2 Evaluate the function for the indicated value, then simplify. 7) f (x) = -3x - 2; find f (a - 2), then simplify as much as possible. A) a - 7 B) -3a + 4 C) -3a - 4 D) a + 4 Evaluate as indicated. 8) If f (x) = 4x 2 + 4x - 0, find and simplify f (2 + x). Solve the problem. A) 4x 2 + 2x + 4 B) 4x 2 + 4x - 2 C) 4 + x D) 4x 2 + 20x + 4 9) At one college, a study found that the average grade point average decreased linearlyaccording to the function g(h) = 3.05-0.05h where h is the number of hours per week spent watching reality shows on television. Compute g(5) and interpret its meaning. A) g(5) = 3.30. On average, watching 5 hours of reality programming per week will increase your GPA by 3.30. B) g(5) = 3.30. This tells us that the average GPA of students that watch 5 hours of reality programming per week is 3.30. C) g(5) = 2.80. On average, watching 5 hours of reality programming per week will decrease your GPA by 2.80. D) g(5) = 2.80. This tells us that the average GPA of students that watch 5 hours of reality programming per week is 2.80. 3
Determine the domain and range of the function. 20) A) Domain: (-, ); Range: (-, -] B) Domain: (-, -]; Range: (-, ) C) Domain: (-, ); Range: [-, ) D) Domain: [-, ); Range: (-, ) 2) A) Domain: (-, ]; Range: [-4, ) B) Domain: [-4, ]); Range [-, - ) C) Domain: (-4, ); Range: (-, ) D) Domain: [-4, ); Range: (-, ] Write the domain in interval notation. 22) f(x) = x + 2 x - 4 A) (-, 4) (4, ) B) (-, -4) (-4, ) C) (-, -2) (-2, ) D) (-, 2) (2, ) 3 23) f(x) = - x A) [, ) B) (-, ) C) (-, ] D) (, ) 4
Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). 24) (3, ); m = 3 A) f(x) = 3x - 8 B) f(x) = 3x + 3 C) f(x) = 3x + 4 D) f(x) = 3x + 25) (6, -3); m = - 5 3 A) f(x) = - 5 3 x - 3 B) f(x) = - 5 3 x - 33 C) f(x) = - 5 3 x + 6 D) f(x) = 5 3 x - 3 Determine the average rate of change of the function on the given interval. 26) f(x) = x - 3 on [4, 7] A) 3 3 B) - 3 3 C) 3 D) - 3 27) f(x) = -2x 2 + 4 on [, 3] A) 8 B) 3 2 C) -8 D) 2 Use the graph to solve the equation and inequality. Write the solution to the inequality in interval notation. 28) a. 3x + 6 = 2x + 5 b. 3x + 6 > 2x + 5 A) a. {3} b. (-, 3} B) a. {-}; b. (-, ) C) a. {-}; b. (-, -) D) a. {3}; b. (3, ) 5
Use the point-slope formula to write an equation of the line that passes through the given points. Write the answer in slope-intercept form (if possible). 29) (-3, -5) and (-8, -3) A) y = - 5 8 x + 79 5 B) y = - 8 5 x + 79 5 C) y = 5 8 x - 5 D) y = 8 5 x - 5 Write an equation of the line satisfying the given conditions. Write the answer in standard form. 30) The line has a slope of - 5 6 A) 5 6 x + y = 20 3 and contains the point (-5, -2). B) 5x + 6y = -37 C) 5x + 6y = 37 D) y = - 5 6 x - 37 6 Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. 3) The line passes through (2, -5) and (, -5). A) y = 0 x - 3 2 B) x = -5 C) y = -5 D) y = 0 x + 3 2 The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. 32) m = 0 7 A) a. m = 0; b. m = 7 0 C) a. m = 0 7 ; b. m = - 7 0 B) a. m = 0; b. m = - 0 7 D) a. m = 0 7 ; b. m = 7 0 Determine if the lines defined by the given equations are parallel, perpendicular, or neither. 33) 3y = -3x - 5-3x = -3y + A) perpendicular B) parallel C) neither 34) 9x - 7y = -5-2 x - 4 3 y = 9 A) neither B) parallel C) perpendicular 6
Use translations to graph the given function. 35) a(x) = x - 2-3 A) B) C) D) 7
36) b(x) = x - 2-3 A) B) C) D) 8
Use transformations to graph the given function. 37) f(x) = -(x - 3) 2 + 2 A) B) C) D) 9
38) f(x) = x + - 2 4 A) B) C) D) Find f(-x) and determine whether f is odd, even, or neither. 39) f (x) = -4x 4 + 5x 2 A) f (-x) = -4x 4 + 5x 2 ; f is even. B) f (-x) = 4x 4-5x 2 ; f is even. C) f (-x) = -4x 4-5x 2 ; f is neither odd nor even. D) f (-x) = -4x 4 + 5x 2 ; f is odd. Determine if the function is odd, even, or neither. 40) f (x) = 2x 2 + 5 x 3-2 A) neither B) odd C) even 0
Graph the function. 4) t(x) = x + 3, for x > 0 x 2, for x 0 A) B) C) D)
42) r(x) = 2 for -5 x < -2-3 for -2 x < 2 3 for x 2 A) B) C) D) 2
Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. 43) A) a. (-, -2) (2, ) b. never decreasing c. (-2, 2) C) a. never increasing b. (-, -2) (2, ) c. (-2, 2) B) a. (-, -) (-, ) b. never decreasing c. (-2, 2) D) a. (3, ) b. (-, 3) c. never constant 3
Identify the location and value of any relative maxima or minima of the function. 44) A) At x = -2, the function has a relative minimum of 2. At x = 0, the function has a relative maximum of 4. B) At x = 2, the function has a relative minimum of -2. At x = 4, the function has a relative maximum of 0. C) At x = -3, the function has a relative maximum of -. At x = 2 the function has a relative minimum of -2. At x = 4 the function has a relative maximum of 0. D) At x = -, the function has a relative maximum of -3. At x = -2, the function has a relative minimum of 2. At x = 0, the function has a relative maximum of 4. Evaluate the function for the given value of x. 45) f (x) = -3x, g(x) = x - 5, (f g)(-3) =? A) (f g)(-3) = -72 B) (f g)(-3) = 72 C) (f g)(-3) = 4 D) (f g)(-3) = -24 46) f (x) = -3x, g(x) = x + 2, A) f g (-5) =? f g (-5) = - 5 f B) g (-5) = - 5 C) f g (-5) = 5 f D) g (-5) = 5 Find f(x + h) - f(x) h 47) f (x) = x 2-3x. for the given function. A) 2x + h - 3 B) 2xh + h 2-3 C) 2x - 3 D) 4
48) f (x) = x + 8 A) C) - 2x + h + 6 (x + 8)(x + h + 8) B) D) - (x + 8)(x + h + 8) 2x + h + 6 Evaluate the function for the given value of x. 49) g(x) = 5x, h(x) = x 3 + 6x, (g h)(4) =? A) 2 22 B) 2 0 C) 76 5 D) 7 5 50) g(x) = 4x - 5, h(x) = 2 x - 8, (h g)() =? A) 8 7-5 B) 8 4-5 C) 6 D) Undefined Find the indicated function and write its domain in interval notation. 5) m(x) = x - 2, n(x) = x -, (m n)(x) =? A) (m n)(x) = x - 2 - ; domain: [2, ) B) (m n)(x) = x - 3; domain: [3, ) C) (m n)(x) = (x - ) x - 2; domain: [2, ) D) (m n)(x) = x 2 + 2; domain: [2, ) 52) n(x) = x + 9, q(x) = A) (q n)(x) = B) (q n)(x) = C) (q n)(x) = D) (q n)(x) =, (q n)(x) =? x + 5 ; domain: (-, 4) (4, ) x + 4 x + 5 x + 5 + 9; domain: (-, -5) (-5, ) + 9; domain: (-, 5) (5, ) ; domain: (-, -4) (-4, ) x + 4 5
Answer Key Testname: MAC 05 - REV T2 - CHAPTER 2 ) B 2) D 3) C 4) D 5) C 6) B 7) B 8) C 9) A 0) A ) C 2) C 3) B 4) B 5) A 6) C 7) B 8) D 9) D 20) C 2) D 22) A 23) B 24) A 25) A 26) C 27) C 28) B 29) D 30) B 3) C 32) C 33) A 34) A 35) A 36) A 37) B 38) C 39) A 40) C 4) A 42) C 43) A 44) C 45) B 46) C 47) A 48) C 49) B 50) D 6 5) B 52) D