n th Roots and Rational Exponents (Part I) Read 5.1 Examples 1-3

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1 HW # n th Roots and Rational Exponents (Part I) Read. Examples - Section. s a. Vocabulary Rewrite the expression t in radical form. Then state the index of the radical.. Complete the Sentence For an integer n greater than, if b n = a, then b is a(n) of a.. Which One Doesn t Belong? Which expression does not belong with the other three? Explain your reasoning. In Exercises 0, find the indicated real nth root(s) of a. (See Example.). n =, a = 8 7. n =, a = 0 9. n =, a = Evaluate the expression without using a calculator. (See Example.).. ( ) 7. 8 Error Analysis Describe and correct the error in evaluating the expression. 9.

2 Using Structure In Exercises, match the equivalent expressions. Explain your reasoning.. ( ) A. B.. ( ). C.. D. Evaluate the expression using a calculator. Round your answer to two decimal places when appropriate. (See Example.) Number Sense Between which two consecutive integers does lie? Explain your reasoning. 9. Problem Solving A weir is a dam that is built across a river to regulate the flow of water. The flow rate Q (in cubic feet per second) can be calculated using the formula Q =.67! h, where! is the length (in feet) of the bottom of the spillway and h is the depth (in feet) of the water on the spillway. Determine the flow rate of a weir with a spillway that is 0 feet long and has a water depth of feet.

3 HW # Properties of Rational Exponents Properties of Radicals (Part I) Read. Examples - Section. In Exercises, use the properties of rational exponents to simplify the expression. (See Example.). ( 9 ) In Exercises 0, use the properties of radicals to simplify the expression. (See Example.) Modeling With Mathematics The surface area S (in square centimeters) of a mammal can be modeled by S = km, where m is the mass (in grams) of the mammal and k is a constant. The table shows the values of k for different mammals. a. Find the surface area of a bat whose mass is grams.

4 HW # Properties of Rational Exponents Properties of Radicals (Part II) Read. Examples,, 6 Section.. Which One Doesn t Belong? Which radical does not belong with the other three? Explain your reasoning. In Exercises 8, write the expression in simplest form. (See Example.) In Exercises 9 6, write the expression in simplest form. (See Example.)

5 HW # Section. Write the expression in simplest form. (See Example.). Properties of Rational Exponents Properties of Radicals (Part III) Read. Examples 6 and 7 Simplify the expression. (See Example 6.) y. m n 0. 6 g h 6 7 h Write the expression in simplest form. Assume all variables are positive. (See Example 7.) a b c 9. 60m n w w w w v 7w v

6 78. How Do You See It? Without finding points, match the functions f ( x) = 6x and 6 g ( x) = 6x with their graphs. Explain your reasoning. 80. Thought Provoking Determine whether the expressions ( x ) 6 and x 6 are equivalent for all values of x. Maintaining Mathematical Proficiency Write a rule for g. Describe the graph of g as a transformation of the graph of f. (Section.7) 87. f ( x) = x, g ( x) = f ( x )

7 HW #6 Graphing and Transforming Radical Functions Read. Examples - Section.. Complete the Sentence Square root functions and cube root functions are examples of functions.. Complete the Sentence When graphing y = a x h + k, translate the graph of y = a x h units and k units. In Exercises 8, match the function with its graph.. f ( x) = x +. h ( x) = x +. f ( x) = x 6. g ( x) = x 7. h ( x) = x + 8. f ( x) = x + Graph the function. Identify the domain and range of the function. (See Example.). g x) = x ( Describe the transformation of f represented by g. Then graph each function. (See Example.). f ( x) = x, g ( x) = x. f ( x) = x, g ( x) = x +

8 8. Error Analysis Describe and correct the error in describing the transformation of the parent square root function represented by g x) = x +. ( 9. Problem Solving The distance (in miles) a pilot can see to the horizon can be approximated by E( n) =. n, where n is the plane s altitude (in feet above sea level) on Earth. The function M ( n) = 0.7E( n) approximates the distance a pilot can see to the horizon n feet above the surface of Mars. Write a rule for M. What is the distance a pilot can see to the horizon from an altitude of 0,000 feet above Mars? (See Example.) In Exercises and, write a rule for g described by the transformations of the graph of f. (See Example.). Let g be a vertical stretch by a factor of, followed by a translation units up of the graph of f ( x) = x +.. Let g be a horizontal shrink by a factor of, followed by a translation units left of the graph of f ( x) = 6x. Write a rule for g that represents the indicated transformation of the graph of f. 7. f ( x) = x, g ( x) = f ( x + )

9 HW #7-8 Solving Radical Equations Read. Examples - (and for the challenge problem) Section. In Exercises, solve the equation. Check your solution. (See Example.). x + = 6 7. x + =. x + 7 =. Modeling With Mathematics Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 6. t , where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 0 centimeters. (See Example.) Solve the equation. Check your solution(s). (See Examples and.). x 6 = x 7. x = x 0

10 Solve the equation. Check your solution(s). (See Examples and.) 9. 8x = x *. x 8 + = x + (challenge problem) 7. Using Structure Explain how you know the radical equation x + = has no real solution without solving it. Maintaining Mathematical Proficiency Let f ( x) = x x + 6. Write a rule for g. Describe the graph of g as a transformation of the graph of f. (Section.7) 70. g ( x) = f ( x ) + 6

11 HW #9 Solving Equations with Rational Exponents Read. Examples -,. Examples -6 Section. Mathematical Connections Find the radius of the figure with the given volume.. V = 6 ft Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. (See Example.) 7. ( 0) 6 x + = 70. x + 6 = 00 Section. 79. Rewriting a Formula a. Solve the formula for the volume of a sphere, V π r =, for r.

12 Section. In Exercises 7, solve the equation. Check your solution(s). (See Examples and 6.) 7. x = 8 9. x + = 0 +. ( x 6) = x. ( x + ) = x + 6. Error Analysis Describe and correct the error in solving the equation.

13 HW #0- Inverses of Functions Read.6 Examples -6 Section.6. Complete the Sentence Functions f and g are inverses of each other provided that f ( g( x)) = and g ( f ( x)) =. Solve y = f (x) for x. Then find the input(s) when the output is. (See Example.). f ( x) = ( x ) 7 Find the inverse of the function. Then graph the function and its inverse. (See Example.). f ( x) = x + Find the inverse of the function. Then graph the function and its inverse. (See Example.). f ( x) = x, x 0 Using Tools Use the graph to determine whether the inverse of f is a function. Explain your reasoning.

14 Determine whether the inverse of f is a function. Then find the inverse. (See Examples and.). f ( x) = x. f ( x) = x + 7. Writing Equations What is the inverse of the function whose graph is shown? Determine whether the functions are inverses. (See Example 6.) 9. f ( x) = x 9, g ( x) = x f ( x) = x, g ( x) = x 9 9. Reasoning You and a friend are playing a number guessing game. You ask your friend to think of a positive number, square the number, multiply the result by, and then add. Your friend s final answer is. What was the original number chosen? Justify your answer. Maintaining Mathematical Proficiency Describe the x-values for which the function is increasing, decreasing, positive, and negative. (Section.) 77.