Name: _ Class: _ Date: Families Multiple Choice Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1 For f( x) = 5x + 1, find f( 4). 19 C 21 1 D 21 2 Suppose f( x) = 4x 2 and g( x) = 2x + 1. Find the value of f( 5) g( 3). 1 5 9 C 2 2 4 7 D 2
3 Determine whether this graph represents a function. If it is a function, state the family it would belong to and find the domain and range. Yes it is a function, it belongs to the exponential family. Ìx x 0 and Range Ì y y 0. Yes it is a function, it belongs to the exponential family. Ìx x R and Range: Ì y y > 0. C D No, it is not a function. Ìx x R and Range: Ì y y > 0. Yes it is a funcition, it belongs to the quadratic family. Ìx x R and Range: {y y 0}. lgebra II Families Pre-Test Page 2
4 Graph the function: y = x + 4. State the translation of the parent function y = x. C Translation: 4 right. D Translation: 4 down Translation: 4 left. Translation: 4 up. lgebra II Families Pre-Test Page 3
5 Write the equation for the translation of y = x 2. y = (x 5) 2 + 2 C y = (x 2) 2 + 5 y = (x + 5) 2 + 2 D y = (x 5) 2 2 6 Compare the graphs of the pair of functions. Describe the family of functions they belong to and then describe how the graph of the second function relates to the graph of the first function. y = x 3 and y = ( x 1) 3 + 2 They are quadratic functions. The second one is y = x 3 shifted 1 right and 2 up. They are quadratic functions. The second one is y = x 3 shifted 1 left and 2 up. C D They are cubic functions. The second one is y = x 3 shifted 1 left and 2 up. They are cubic functions. The second one is y = x 3 shifted 1 right and 2 up. 7 The Smiths rented a minivan for their family vacation. When they returned from vacation, the total bill for the van was $575 The standard weekly rate from the rental company is $355 plus $55 for each additional day of usage. Write a linear function to represent this situation and then use that function to determine how many additional days did the Smiths have the minivan. y = 355 + 55x; 5 days C y = 575 + 55x; 3 days y = 575 + 55x; 6 days D y = 355 + 55x; 4 days lgebra II Families Pre-Test Page 4
8 If f(x) = x 2 + 1, then f(f(x)) = 2x 2 + 2 C x 4 + 2x 2 + 1 2x 2 + 1 D x 4 + 2x 2 + 2 9 Given a function f(x), which of the following represents a vertical shift of 2 units upward, followed by a reflection across the y-axis? f( x) + 2 C f(x) + 2 f(2 x) D f(x 2) 10 balloon takes off from a location that is 158 ft above sea level. It rises 56 ft/min. Write an equation to model the balloon s elevation h as a function of time t. t(h)= 158h + 56 C h(t) = 158t + 56 h(t) = 56t + 158 D t(h) = 56h + 158 11 Choose the correct range for the function f(x) = 250 + 10x where 0 x 4 and x is an integer. 0, 1, 2, 3, 4 C 250, 260, 270, 280, 290 0, 1, 2, 3 D 250, 260, 270, 280 12 Name the family of functions that the graph of y = 3 x represents: linear C power exponential D quadratic 13 Let h(x) = 5x 3 + 2x 2 7x + 9 and f(x) = 4x 3 + 3x 2 + 2x + 1, which of the following equals h(x) f(x): x 3 x 2 5x 8 C x 3 + 5x 2 9x + 1 9x 3 x 2 9x + 8 D 9x 3 + 5x 2 9x + 1 lgebra II Families Pre-Test Page 5
14 Which family of functions does y = x + 3 + 2 belong to? What is the domain and range of the function? square root function, C square root function, Ìx x 3, Range: Ì y y 2 Ìx x > 3, Range: Ì y y 0 square function D square function Ìx x 3, Range: Ì y y 2 Ìx x R Range: Ì y y 2 15 Let f(x) = 3x 5 and g(x) = x 2, find f(g(1)): -2 C 4 2 D -4 16 Determine the inverse function to f(x) = x 3 + 5. f 1 3 (x) = x f 1 3 (x) = x + 5 C f 1 3 (x) = x 5 5 D f 1 3 (x) = x + 5 17 If f(x) = x 7 and g(x) = 4 x, what is the value and domain of the function f(x) g(x)? x 7 4 x ; {x x < 4} C x 7 ; {x x > 4} 4 x 4 x x 7 ; {x x 4} D 4 x ; {x x 4} x 7 lgebra II Families Pre-Test Page 6
For the next three questions, use the following information about a rectangular rug: the width of the rug is (x + 2) and the length is (2x - 3). 18 What family of functions would best represent the perimeter of the rectangle? What family of functions would best represent the area of the rectangle? perimeter = quadratic, area = linear C perimeter = linear, area = square root perimeter = quadratic, area = cubic D perimeter = linear, area = quadratic 19 What equation would model the perimeter of the rectangle? What equation would model the area of the rectangle? P = 3x 1 = 2x 2 6 P = 6x 2 = 2x 2 6 C P = 3x 1 = 2x 2 + x 6 D P = 6x 2 = 2x 2 + x 6 20 You have enough paper to make the width 8 inches. What is the value of x? What is the perimeter? What is the area? x = 6, P = 17, = 66 C x = 6, P = 34, = 72 x = 10, P = 29, = 194 D x = 10, P = 58, = 204 21 Let f(x) = 7x 2 + 3 and g(x) = 5x 2 + 8, which of the following is equal to f(x) + g(x)? 12x 2 + 11 C 12x 2 + 5 12x 4 + 11 D 12x 4 + 5 22 Which of the following form can be used to represent a logarithmic function? f(x) = x 2 + x + C C f(x) = log(x + C) + D f(x) = tan(x) D f(x) = x lgebra II Families Pre-Test Page 7
23 Which of the following equations represent a function? x 2 + y 2 = 25 C y = x 2 x 2 y 2 = 25 D x = y 2 24 Determine the inverse to the function: y = (x 3) 2 + 5. Is the inverse a function? What is the domain of the inverse? y = ± x 5 + 3, no it is not a function, Ìx x 5 y = ± x + 5 3, no it is not a function, Ìx x 5 C y = ± x 5 + 3, yes it is a function, Ìx x 5 D y = ± x + 5 3, yes it is a function, Ìx x 5 25 If f(x) = x 2 + x 1 and g(x) = x + 3, what is f(x) g(x)? 3x 2 + 3x 3 C x 3 + 4x 2 + 2x 3 x 3 + x 2 x D x 3 2x 2 4x 3 26 Find the inverse of the function, y = 2x - 4. What are the x and y-intercepts of both functions? y = 2x - 4; x-inter: (2, 0) y-inter: (0, -4) y = 2x + 4; x-inter: (2, 0) y-inter: (0, 4) y = 2x - 4; x-inter: (2, 0) y-inter: (0, -4) y = 0.5x + 2; x-inter: (-4, 0) y-inter: (0, 2) C y = 2x - 4; x-inter: (-4, 0) y-inter: (0, 2) y = 0.5x + 2; x-inter:(2, 0) y-inter:(0, -4) D y = 2x - 4, x-inter: (2, 0) y-inter: (0, -4) y = 2x + 4, x-inter: (4, 0), y-inter: (0, 2) lgebra II Families Pre-Test Page 8