m x x Assignment #2 MAT121 Summer 2017 NAME:

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1 Assignment # MAT11 Summer 017 NAME: Directions: Do ALL of your work on THIS handout in the space provided! Circle your final answer! On problems that your teacher would show work on be sure that you also show work on! This assignment is DUE on or before 8:00 a.m. Wednesday May 1 st (see your syllabus for late penalty!)..1 (continued) Introduction to Rational Expressions Reduce the expression to lowest terms. 1. 0xy 16 xy. 10m m m x 0 x 4 4. y y6 y y x x. Multiplication and Division of Rational Expressions Multiply or divide as indicated x 1 x 6x 4x 8

2 8. 4a16 a4 a1 a10 9. p p 1 16 p 1 4 p1 p x x 1 x x 9 x 8x 16 x 1x 1. Least Common Denominator Fill in the blank to convert the expressions to equivalent expressions with the indicated denominator x x x x 4 Identify the LCD. 7 1., x, x 1 x x x 4 1. x, 9 4 x x x

3 Find the LCD then convert each expression to an equivalent expression with the denominator equal to the LCD. On #17 and #18 multiply out the numerators of your equivalent expression but NOT the denominators! 16. 6b, ab 4ab 6, 17. x x 4 x 4 x x x4, x x1.4 Addition and Subtraction of Rational Expressions. Add or subtract the expressions with like denominators, simplify as much as possible 19. b 1 b b 0. x x 6 x6 x 6 Add or subtract the expressions with unlike denominators, simplify as much as possible x x 4x 6. y 6 y y y

4 . y y 4 y y1 y 4y 1 4y 9y. a 1 9a 6a 8 a a 8

5 . Rational Equations. Solve the rational equations. Be sure to check all solutions. If a solution does not check state that it is extraneous. 6. w w 7. w w x 1 x8 x x 4 x 8. x 1 x x x x Solve the following proportions. 9. x x x1 x

6 .6 Applications of Rational Equations and Proportions 1. A lawn fertilizer calls for pounds for 10 square feet. At this rate, how many pounds are required for 8 square feet?. A map has a scale of 0 miles equals 1 inch. How many inches will two cities be apart on the map if they are actually 140 miles apart?. Jess answered 8 of 10 trivia questions correct. At this rate how many questions out of 0 will she answer correctly? 4. A boat travels 10 miles upstream against the current in the same time it takes to go 0 miles downstream with the current. If the speed of the current is miles per hour, find the speed of the boat in still water.. A plane flies 400 miles with the wind in the same time it takes to fly 0 miles against the wind. If the speed of the wind is 0 miles per hour, find the speed of the plane in still air.

7 .1 Definition of nth Root Evaluate the roots without a calculator. Identify those that are not real numbers. NO decimal answers should be given! Use a calculator to evaluate the expression, round to three decimal places Simplify without a calculator. Make no assumptions regarding variables ( ) 0. x x Simplify the radical expressions. Use absolute values when necessary. 4. 8x y 1 z x. Simplify the expressions. Assume all variables are positive real numbers, so no absolute values will be needed in any of the answers. 6. 8x y 1 z x 7.

8 . Rational Exponents. Write the expression using positive exponents and radical notation, then simplify. Work should be shown on all of these! 1 9. ( ) Simplify the expression using the properties of rational exponents. Write the final answer using positive exponents. Work should be shown on all of these! a a 1 Use a calculator to approximate the expressions and round to 4 decimal places Properties of Radicals For this point forward, assume that all variables represent positive real numbers unless stated otherwise. Use the multiplication property of radicals (and rules of exponents) to multiply the expressions. Then simplify the result. 66. ab a b 67. (x 1) 18(x 1) 8 Use the division property of radicals (and rules of exponents) to divide the expression. Then simplify the result x x x 1 x 1 9

9 Simplify the radicals. No decimal answers! x y z 74. 7a b c xy 8.4 Graphing square and cube root functions. Sketch the graph of each function. Create a table of values and label points. You may use a calculator and should round to two decimal places when needed. 76. f x x f x x f x x 1

10 79. f x x 1 Use your graphs for to find the domain and range of each function. Write your answer using interval notation. 80. f x x 4 D: R: 81. f x x 1 D: R: 8. f x x 1 D: R: 8. f x x 1 D: R: