Absolute Value and Reciprocal Functions Multiple Choice Identify the choice that best completes the statement or answers the question. ____1. Evaluate the expression . A –67.5 C 64.5 B –64.5 D 67.5 ____2. Determine the value of the absolute value expression A –5 C –85 B 85 D 5 ____3. Evaluate . A 17 C 35 B 21 D 25 . ____4. The graph of is y A –10 –8 –6 –4 y C 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –6 –4 8 10 x 2 4 6 8 10 x 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 –2 –2 6 y D 16 –10 –8 4 –4 y B 2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 ____5. What are the domain and range of A C B D ? ____6. Determine the solution to 17 1 or x = 2 2 17 1 B x = or x = 2 2 A x = ____7. Solve A x = C no solution D x = 1 2 . C x = 10 B x = ± 2 10 , x = ± 2 ± D x = 10 , x = 2 ____8. Which graph represents the reciprocal of y A –6 –4 y C 10 –10 –8 ? 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 –6 –6 –8 –8 –10 –10 2 4 6 8 10 x y B 10 –10 –8 –6 –4 y D 10 8 8 6 6 4 4 2 2 –2 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 –2 –4 –4 –6 –6 –8 –8 –10 –10 2 4 ____9. Which graph represents the reciprocal of y A –5 –4 –3 –2 4 3 2 2 1 1 2 3 4 5 x –4 –3 –2 –4 –3 –2 –1 –1 –2 –3 –3 –4 –4 –5 –5 4 3 3 2 2 1 1 1 2 3 4 5 x 2 3 4 5 x 1 2 3 4 5 x 5 4 –1 –1 1 y D 5 –5 –5 –2 y B x 5 3 1 10 y 4 –1 –1 8 ? C 5 6 –5 –4 –3 –2 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5 ____10. The equation of the vertical asymptote for the reciprocal of y = 8x – 4 is A x = B x = 2 1 2 C x = 1 2 D x =2 Short Answer 1. Evaluate each absolute value expression. a) b) c) d) 2. Given the graph of : a) sketch the graph of b) state the domain and range c) express as a piecewise function. y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 1 2 3 4 5 x 3. Consider the function . a) Express the function in vertex form, . b) Sketch the graph of the function. Label the vertex and x-intercepts. c) What are the domain and range? y 9 8 7 6 5 4 3 2 1 –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 –6 –7 –8 –9 1 2 3 4 5 6 7 8 9 x Problem 1. Graph the reciprocal function a) the equations of any asymptotes b) the domain and range and determine Absolute Value and Reciprocal Functions Answer Section MULTIPLE CHOICE 1. ANS: NAT: 2. ANS: NAT: 3. ANS: NAT: 4. ANS: NAT: 5. ANS: NAT: 6. ANS: NAT: 7. ANS: NAT: 8. ANS: NAT: 9. ANS: NAT: 10. ANS: NAT: C RF 2 D RF 2 B RF 2 D RF 2 B RF 2 C RF 2 C RF 2 D RF 11 A RF 11 C RF 11 PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: 1 DIF: Easy Absolute Value 1 DIF: Average Absolute Value 1 DIF: Difficult Absolute Value 1 DIF: Average Absolute Value Functions 1 DIF: Easy Absolute Value Functions 1 DIF: Average Absolute Value Equations 1 DIF: Average Absolute Value Equations 1 DIF: Average Reciprocal Functions 1 DIF: Average Reciprocal Functions 1 DIF: Easy Reciprocal Functions OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: OBJ: KEY: Section 7.1 evaluating expressions Section 7.1 evaluating expressions Section 7.1 evaluating expressions Section 7.2 graphing | linear Section 7.2 domain | range | linear Section 7.3 linear | no solution Section 7.3 algebraic solution | quadratic Section 7.4 linear | graphing Section 7.4 quadratic | graphing Section 7.4 vertical asymptote SHORT ANSWER 1. ANS: a) b) c) d) PTS: 1 DIF: Average OBJ: Section 7.1 NAT: RF 2 TOP: Absolute Value 2. ANS: a) KEY: evaluating expressions y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x –2 –3 –4 –5 b) The domain is all real numbers or The range is all non-negative values of y, or . . c) PTS: 1 DIF: Average TOP: Absolute Value Functions 3. ANS: a) OBJ: Section 7.2 NAT: RF 2 KEY: linear | graphing | domain | range | piecewise function b) y 9 8 7 6 5 4 (4, 3) 3 2 1 (2.8, 0) –1 –1 1 2 (5.2, 0) 3 4 5 6 7 8 9 x c) The domain is all real numbers or . The range is all non-negative values of y, or PTS: 1 DIF: Difficult TOP: Absolute Value Equations . OBJ: Section 7.2 NAT: RF 2 KEY: graphing | quadratic | vertex form | domain | range PROBLEM 1. ANS: y 9 8 7 6 5 4 3 2 1 –7 –6 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 –6 –7 –8 –9 1 2 3 4 5 6 7 x a) There are vertical asymptotes at and and a horizontal asymptote at y = 0. b) Domain Range PTS: 1 DIF: Easy TOP: Reciprocal Functions OBJ: Section 7.4 NAT: RF 11 KEY: quadratic | graphing

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