SOLUTION: The domain of a square root function only includes values for which the radicand is nonnegative.
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1 19. Graph each function. State the domain and range. 21. The domain of a square root function only includes values for which the radicand is nonnegative. esolutions Manual - Powered by Cognero Page 1
2 23. The domain of a square root function only includes values for which the radicand is nonnegative. Find f ( 3) to determine the lower limit of the range. 25. The domain of a square root function only includes values for which the radicand is nonnegative. Find f (5) to determine the lower limit of the range. f(4) = 6 esolutions Manual - Powered by Cognero Page 2
3 27. The domain of a square root function only includes values for which the radicand is nonnegative. Find f (1) to determine the upper limit of the range. f(4) = SKYDIVING The approximate time t in seconds that it takes an object to fall a distance of d feet is given by. Suppose a parachutist falls 11 seconds before the parachute opens. How far does the parachutist fall during this time? Substitute t = 11 in the equation and find d. The parachutist falls 1936 feet. esolutions Manual - Powered by Cognero Page 3
4 Graph each inequality. 31. Graph the boundary. Since the inequality symbol is <, the boundary should be dashed. The domain is domain.. Because y is less than, the shaded region should be below the boundary and within the 33. Graph the boundary. Since the inequality symbol is, the boundary line should be solid. The domain is the domain.. Because y is greater than, the shaded region should be above the boundary and within esolutions Manual - Powered by Cognero Page 4
5 35. Graph the boundary. Since the inequality symbol is >, the boundary line should be dashed. The domain is the range.. Because y is greater than, the shaded region should be above the boundary and within 37. Graph the boundary. Since the inequality symbol is, the boundary line should be solid. The domain is d within the range.. Because y is less than, the shaded region should be below the boundary an esolutions Manual - Powered by Cognero Page 5
6 39. PHYSICS The kinetic energy of an object is the energy produced due to its motion and mass. The formula for kinetic energy, measured in joules j, is E = 0.5mv 2, where m is the mass in kilograms and v is the velocity of the object in meters per second. a. Solve the above formula for v. b. If a 1500-kilogram vehicle is generating 1 million joules of kinetic energy, how fast is it traveling? c. Escape velocity is the minimum velocity at which an object must travel to escape the gravitational field of a planet or other object. Suppose a 100,000-kilogram ship must have a kinetic energy of Jupiter. Estimate the escape velocity of Jupiter. a. Solve for v. joules to escape the gravitational field of b. Substitute E = 1,000,000 and m = Find v. c. Substitute and m = 100,000. Find v. esolutions Manual - Powered by Cognero Page 6
7 41. Write the square root function represented by each graph. The graph represents the function. 43. The graph represent the function. esolutions Manual - Powered by Cognero Page 7
8 Determine whether each pair of functions are inverse functions. Write yes or no. 59. The functions f (x) and g(x) are inverses if and only if. Since, f and g are not inverses. 61. TIME The formula converts minutes m to hours h, and converts hours h to days d. Write a function that converts minutes to days. esolutions Manual - Powered by Cognero Page 8
9 Determine whether each number is rational or irrational can be written in the form, for example, as follows: Therefore, it is a rational number The number can be written in the form, for example, as follows: Therefore, it is a rational number. esolutions Manual - Powered by Cognero Page 9
6-3 Square Root Functions and Inequalities. Identify the domain and range of each function. ANSWER: ANSWER:
Identify the domain and range of each function. 7. 1. 3. Graph each function. State the domain and range. 5. Graph each inequality. 9. esolutions Manual - Powered by Cognero Page 1 11. Graph each function.
Study Guide and Review - Chapter 6. Choose a word or term that best completes each statement.
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2. Simplify each expression. 10. MULTIPLE CHOICE Which expression is equivalent to? A B 4. C D 6. 8. 12. The correct choice is D. Simplify each expression. esolutions Manual - Powered by Cognero Page 1
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Solve each equation. 7. 1. 20 2 8. 2. 3. 4. 5. 23 13 12 29 9. 10. 11. 19 49 No solution 6. 13 12. 9 esolutions Manual - Powered by Cognero Page 1 13. CCSS REASONING The time T in seconds that it takes
10-2 Simplifying Radical Expressions. Simplify each expression. 1. SOLUTION: 2. SOLUTION: 3. SOLUTION: 4. SOLUTION: 5. SOLUTION:
- Simplifying Radical Expressions Simplify each expression.... 4. 5. Page - Simplifying Radical Expressions 5. 6. 7. 8. 9. Page - Simplifying Radical Expressions 9.. MULTIPLE CHOICE Which expression is
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Write each set of numbers in set-builder and interval notation, if possible. 1. x > 50 The set includes all real numbers greater than 50. In set-builder notation this set can be described as {x x > 50,
The function is defined for all values of x. Therefore, the domain is set of all real numbers.
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