Determine if the lines defined by the given equations are parallel, perpendicular, or neither. 1) -4y = 2x + 5

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1 Review test 3 -College Algebra Math Spring Houston Community College Name Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the lines defined by the given equations are parallel, perpendicular, or neither. 1) -4y = 2x + 5-4x = 8y + 3 A) neither B) perpendicular C) parallel 2) -4y = 3x + 3-6x = 8y + 7 A) parallel B) neither C) perpendicular 1) 2) Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. 3) Passes through (4, 4) and is perpendicular to the line defined by -5x + 4y = -6 3) A) 4x + 5y = 36 B) -5x - 4y = -36 C) 5x - 4y = 4 D) 4x - 5y = -4 Solve the problem. 4) A bakery makes and sells pastries. The fixed monthly cost to the bakery is $770. The cost for labor, taxes, and ingredients for the pastries amounts to $0.90 per pastry. The pastries sell for $1.60 each. a. Write a linear profit function representing the profit for producing and selling x pastries. b. Determine the break-even point for the bakery. A) a. P(x) = 0.7x + 770; b. 1,100 pastries B) a. P(x) = 1.60x + 770; b. 481 pastries C) a. P(x) = 0.7x - 770; b. 1,100 pastries D) a. P(x) = 1.60x - 770; b. 481 pastries 5) At the Jumping Jack cookie factory, quality assurance inspectors remove broken or otherwise defective cookies from a moving conveyor belt prior to packaging. Based on past studies, the plant manager knows that the inspectors eliminate 98% of the defective cookies at a conveyor belt speed of 9 feet per minute. As the belt speed increases, the factory can produce more cookies per hour, but at the cost of lower quality of the packaged product. Inspectors collect only 60% of defective cookies at a belt speed of 18 feet per minute. 4) 5) 1

2 a. Find an equation of the line through the given points. Write the equation in slope-intercept form. Round the slope and y-intercept each to 1 decimal place. b. Use the equation from part (b) to predict the efficiency of the inspectors at a belt speed of 15 feet per minute. Round to the nearest percent. A) a. y = x b. 66.5% at a belt speed of 15 feet per minute. B) a. y = x b. 73% at a belt speed of 15 feet per minute. C) a. y = x b. 73% at a belt speed of 15 feet per minute. D) a. y = x b. 66.5% at a belt speed of 15 feet per minute. 2

3 Use transformations to graph the given function. 6) f(x) = -x - 4 6) A) B) C) D) 3

4 A function g is given. Identify the parent function. Then use the steps for graphing multiple transformations of functions to list, in order, the transformations applied to the parent function to obtain the graph of g. 7) g(x) = 1 5 (x + 1.3) ) A) Parent function: f (x) = x 2 ; Shift the graph of f to the right 1.3 units, stretch the graph vertically by a factor of 5, and shift the graph upward by 2.5 units. B) Parent function: f (x) = x 2 ; Shift the graph of f to the left 1.3 units, strech the graph vertically by a factor of 5, and shift the graph downward by 2.5 units. C) Parent function: f (x) = x 2 ; Shift the graph of f to the right 1.3 units, shrink the graph vertically by a factor of 1, and shift the graph upward by 2.5 units. 5 D) Parent function: f (x) = x 2 ; Shift the graph of f to the left 1.3 units, shrink the graph vertically by a factor of 1, and shift the graph downward by 2.5 units. 5 The graph of y = f (x) is given. Graph the indicated function. 8) Graph y = f (-x) - 4 8) A) B) 4

5 C) D) Write a function based on the given parent function and the transformations in the given order. 9) Parent function y = 1 x 9) 1. Stretch vertically by a factor of Reflect across the x-axis. 3. Shift downward 9 units. A) y = 6 x + 9 B) y = - 6 x - 9 C) y = 6 x - 9 D) y = - 6 x + 9 Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these. 10) y = x ) A) y-axis B) x-axis C) x-axis, y-axis, and origin D) none of these Write a function based on the given parent function and the transformations in the given order. 11) Parent function y = 1 x 11) 1. Stretch vertically by a factor of Reflect across the x-axis. 3. Shift downward 8 units. A) y = 4 x + 8 B) y = - 4 x - 8 C) y = - 4 x + 8 D) y = 4 x - 8 5

6 Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these. 12) y = x ) A) x-axis B) y-axis C) x-axis, y-axis, and origin D) none of these Determine if the function is odd, even, or neither. 13) f (x) = x 3 7x 2 13) A) Neither B) Odd C) Even 6

7 Use the given information to a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. x for x < 4 14) f (x) = -x for x 4 A) domain: (-, ) range: (-4, ) B) domain: (-, ) range: (-, -4] [0, ) 14) C) domain: (-, ) range: (-, -4) (0, ) D) domain: (-, ) range: [-4, ) 7

8 15) f (x) = x for x < 1 -x for x 1 A) domain: (-, ) range: (-, -1) (0, ) B) domain: (-, ) range: (-, -1] [0, ) 15) C) domain: (-, ) range: [-1, ) D) domain: (-, ) range: (-1, ) Find the indicated function and write its domain in interval notation. 9 16) f (x) = x 2, g(x) = 4 - x, ( f g)(x) =? 16) x A) x 2-11 ; (-, 11) ( 11, ) B) - 9 ; (-, -7) (-7, ) x + 7 C) - 9 ; (-, -7) (-7, 4] x + 7 D) x x 2 ; (-, 11) ( 11, 4]

9 Write the function in vertex form and determine the range. 17) f (x) = -3x x ) A) f (x) = -3(x - 3) 2-6 Range: [3, ) C) f (x) = -3(x + 3) 2-6 Range: (-, -6] B) f (x) = -3(x + 3) 2-6 Range: [3, ) D) f (x) = -3(x - 3) 2-6 Range: (-, -6] 9

10 Answer Key Testname: REVIEW TEST 3 1) C 2) A 3) A 4) C 5) B 6) C 7) D 8) B 9) B 10) D 11) B 12) D 13) B 14) B 15) B 16) C 17) D 10