5.1 Practice A. Name Date ( ) 23 15, , x = 20. ( ) 2

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1 Name Date. Practice A In Exercises, find the indicated real nth root(s) of a.. n =, a =. n =, a = 9. n =, a = 8 In Exercises 9, evaluate the expression without using a calculator ( ) In Exercises 0, evaluate the expression using a calculator. Round your answer to two decimal places when appropriate. 0. 6,807. 6, In Exercises 6 and 7, find the radius of the figure with the given volume. 6. V = 76 in. 7. V = 7 m h = in. r r In Exercises 8, find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. 8. x = ( 7) x + = 000. x 6 = 0 x = 0. ( ) x =. 9x =. When the average price of an item increases from p to p over a period of n n years, the price p is given by p = p( r + ), where r is the annual rate of inflation (in decimal form). Find the annual rate of inflation when the price of a loaf of bread was $.9 in 970 and $.9 in Algebra Copyright Big Ideas Learning, LLC

2 Name Date. Practice A In Exercises 6, use the properties of rational exponents to simplify the expression.. ( 7 ). ( ) ( ) 7 7 In Exercises 7, use the properties of radicals to simplify the expression In Exercises 8, write the expression in simplest form In Exercises 9, simplify the expression ( ) + 79 ( ) The volume of a cube is 80 cubic centimeters. a. Use exponents to solve the formula for the volume V of a cube with side length s, V = s, for s. b. Substitute the expression for s from part (a) into the formula for the surface area of a cube, S = 6 s. c. Substitute the volume of the given cube into the formula found in part (b) to find the surface area, S. Simplify, if possible. Copyright Big Ideas Learning, LLC Algebra

3 Name Date. Practice A In Exercises 6, graph the function. Identify the domain and range of the function.. gx ( ) = x+. hx ( ) = x. f ( x) = x. hx ( ) = x. f ( x) = x 6. g ( x) = x + In Exercises 7, describe the transformation of f represented by g. Then graph each function. 7. f( x) = x; g( x) = x + 8. ( ) ( ) f x = x; g x = x + 9. f ( x) = x; g( x) = x 0. ( ) ( ) f x x g x x. f ( x) = x ; g( x) = ( x). ( ) ; ( ) = ; = + f x = x g x = x In Exercises, use a graphing calculator to graph the function. Then identify the domain and range of the function.. f ( x) = x x. ( ) =. ( ) g x x x hx = x + x In Exercises 6 and 7, write a rule for g described by the transformations of the graph of f. 6. Let g be a vertical shrink by a factor of, followed by a translation units right of the graph of f( x) = x Let g be a reflection in the x-axis, followed by a translation units down of the graph of f ( x) = x +. In Exercises 8 and 9, use a graphing calculator to graph the equation of the parabola. Identify the vertex and the direction that the parabola opens. 8. y = x 9. y = x + 6 In Exercises 0 and, use a graphing calculator to graph the equation of the circle. Identify the radius and the intercepts. 0. x y 6 + =. y = x 8 Algebra Copyright Big Ideas Learning, LLC

4 Name Date. Practice A In Exercises 6, solve the equation. Check your solution.. x =. 6x + = 9. x + 0 =. x 8 =. 6x + = x 6 = 7. Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 6. t + 7.8, where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 00 centimeters. In Exercises 8, solve the equation. Check your solution(s). 8. x 8 = x 9. x = x 7 0. x + = x +. 8x + 7 = x +. 9x = x. x = x + 9 In Exercises 6, solve the equation. Check your solution(s).. x = x + = 6. ( x ) + = x 7. Describe and correct the error in solving the equation. x + = 8 x + = x = x = In Exercises 8 0, solve the inequality. 8. x 9. x 7 0. x > 0. The length (in inches) of a standard nail can be modeled by d is the diameter (in inches) of the nail. = d, where a. What is the diameter of a standard nail that is inches long? b. What is the diameter of a standard nail that is inches long? c. The nail in part (b) is twice as long as the nail in part (a). Is the diameter twice as long? Explain. Copyright Big Ideas Learning, LLC Algebra 6

5 Name Date. Practice A In Exercises and, find ( f + g)( x) and ( f g)( x) of each. Then evaluate f f x = x g x = x x =. ( ) ( ) and state the domain + g and f g for the given value of x. ; ; 8 f x = x + x g x = x x + x = 9 ; 7;. ( ) ( ) f In Exercises, find ( fg)( x) and ( x) g and state the domain of each. Then evaluate fg and f for the given value of x. g f x = x ; g x = x ; x = 9. ( ) ( ) f x = x g x = x x =. ( ) ( ). ( ) ( ) 0 ; ; 8 f x = x g x = x x = ; ; 7 In Exercises 6 and 7, use a graphing calculator to evaluate ( f + g)( x), ( f g)( x) f g ( fg)( x ), and ( x), when x =. Round your answers to two decimal places. 6. f ( x) = x ; g( x) = 0x 7. ( ) ( ) 8. Describe and correct the error in stating the domain. ( ) ( ) f x = x + and g x = x The domain of ( f + g)( x) is all real numbers. f x = x ; g x = 6x 9. The growth of mold in Specimen A can be modeled by At () = t. The growth 6 of mold in Specimen B can be modeled by B () t = t. a. Find ( A B)( t). b. Explain what the function ( A B)( t) represents. 68 Algebra Copyright Big Ideas Learning, LLC

6 Name Date.6 Practice A In Exercises, solve y f( x) = for x. Then find the input(s) when the output is.. f( x) = x +. ( ) f x = x. f ( x) = 8x In Exercises 6, find the inverse of the function. Then graph the function and its inverse.. f ( x) = x. f( x) = x 6. f( x) 7. Find the inverse of the function ( ) = x f x = x by switching the roles of x and y and solving for y. Then find the inverse of the function f by using inverse operations in the reverse order. Which method do you prefer? Explain. 8. Determine whether each pair of functions f and g are inverses. Explain your reasoning. a. b. x 0 f(x) 9 x f(x) 9 7 x 0 g(x) 0 x 9 7 g(x) In Exercises 9, find the inverse of the function. Then graph the function and its inverse. 9. f( x) = 9 x, x 0 0. f( x) = 6 x, x 0. f( x) = ( x + ) In Exercises and, use the graph to determine whether the inverse of f is a function. Explain your reasoning Copyright Big Ideas Learning, LLC Algebra 7