Study Guide and Review - Chapter 6. Choose a word or term that best completes each statement.
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1 Choose a word or term that best completes each statement. 1. If both compositions result in the,then the functions are inverse functions. identity function 2. In a(n), the results of one function are used to evaluate a second composition of functions 3. Radicals are if both the index and the radicand are identical. like radical expressions 4. When there is more than one real root, the nonnegative root is called the. principal root 7. Two relations are if and only if one relation contains the element (b, a) when the other relation contains the element (a, b). inverse relations 8. When solving a radical equation, sometimes you will obtain a number that does not satisfy the original equation. Such a number is called a(n). extraneous solution 9. The square root function is a type of. 10. radical function Find and. 5. To eliminate radicals from a denominator or fractions from a radicand, you use a process called. rationalizing the denominator 6. Equations with radicals that have variables in the radicands are called. radical equations esolutions Manual - Powered by Cognero Page 1
2 MEASUREMENT The formula converts 13. yards y to feet f and converts inches n to feet f. Write a composition of functions that converts yards to inches. Substitute 3y for f into the second equation and solve for n. esolutions Manual - Powered by Cognero Page 2
3 Find the inverse of each Then graph the function and its inverse Rewrite f (x) as y = 5x 6. Interchange the variables and solve for y. Rewrite f (x) as y = 3x 5. Interchange the variables and solve for y. -1 Replace y with f (x). Graph the function and its inverse in the same coordinate plane. Replace y with f -1 (x). Graph the function and its inverse in the same coordinate plane. esolutions Manual - Powered by Cognero Page 3
4 Rewrite f (x) as Interchange the Rewrite f (x) as Interchange the variables variables and solve for y. and solve for y. Replace y with f -1 (x). Graph the function and its inverse in the same coordinate plane. Replace y with f -1 (x). Graph the function and its inverse in the same coordinate plane. esolutions Manual - Powered by Cognero Page 4
5 Rewrite f (x) as Interchange the variables and solve for y. Rewrite f (x) as Interchange the variables and solve for y. Replace y with f -1 (x). Graph the function and its inverse in the same coordinate plane. Replace y with f -1 (x). Graph the function and its inverse in the same coordinate plane. esolutions Manual - Powered by Cognero Page 5
6 23. SHOPPING Samuel bought a computer. The sales tax rate was 6% of the sale price, and he paid $50 for shipping. Find the sale price if Samuel paid a total of $1322. Let x be the sale price of the computer. 25. Graph the function. The equation that represent the situation is Solve for x. 24. The sale price is $1200. Use the horizontal line test to determine whether the inverse of each function is also a Graph the function. 26. No horizontal line can be drawn so that it passes through more than one point. The inverse of this function is a Graph the function. The horizontal line drawn passes through more than one point. So, the inverse of this function is not a The horizontal line drawn passes through more than one point. So, the inverse of this function is not a esolutions Manual - Powered by Cognero Page 6
7 Graph the function. Graph of the function. The horizontal line drawn passes through more than one point. The inverse of this function is not a The horizontal line drawn passes through more than one point. So, the inverse of this function is not a 28. Graph the function. 30. FINANCIAL LITERACY During the last month, Jonathan has made two deposits of $45, made a deposit of double his original balance, and has withdrawn $35 five times. His balance is now $189. Write an equation that models this problem. How much money did Jonathan have in his account at the beginning of the month? Let x be the original balance in Jonathan s account. The equation that represents the situation is Solve for x. The horizontal line y = 3 drawn passes through more than one point. So, the inverse of this function is not a The original balance in the account is about $ esolutions Manual - Powered by Cognero Page 7
8 Graph each State the domain and range Identify the domain. Identify the domain. Write the radicand as greater than or equal to 0. Write the radicand as greater than or equal to 0. Make a table of values for and graph the Make a table of values for and graph the The domain is, and the range is The domain is, and the range is esolutions Manual - Powered by Cognero Page 8
9 Identify the domain. Write the radicand as greater than or equal to 0. Identify the domain. Write the radicand as greater than or equal to 0. Make a table of values for and graph the Make a table of values for and graph the The domain is, and the range is The domain is, and the range is esolutions Manual - Powered by Cognero Page 9
10 Identify the domain. Write the radicand as greater than or equal to 0. Identify the domain. Write the radicand as greater than or equal to 0. Make a table of values for and graph the Make a table of values for and graph the The domain is, and the range is The domain is, and the range is esolutions Manual - Powered by Cognero Page 10
11 37. GEOMETRY The area of a circle is given by the formula. What is the radius of a circle with an area of 300 square inches? 39. Substitute 300 for A in the formula and solve for r. The radius of the circle is about 9.8 in Graph each inequality. Simplify. 41. esolutions Manual - Powered by Cognero Page 11
12 PHYSICS The velocity v of an object can be defined as, where m is the mass of an object and K is the kinetic energy in joules. Find the velocity in meters per second of an object with a mass of 17 grams and a kinetic energy of 850 joules. 45. Substitute 17 for m and 850 for K in the formula and solve for v: The velocity of the object is 10 m/s. 46. esolutions Manual - Powered by Cognero Page 12
13 Simplify esolutions Manual - Powered by Cognero Page 13
14 57. Simplify each expression GEOMETRY What are the perimeter and the area of the rectangle? 60. Substitute for length and for width in the perimeter formula and simplify. 61. The perimeter of the rectangle is units. The area of the rectangle is square units. esolutions Manual - Powered by Cognero Page 14
15 Simplify each expression. 65. GEOMETRY What is the area of the circle? 62. Substitute and simplify.] for r in the area of circle formula 63. So, the area of the circle is units 2. Solve each equation esolutions Manual - Powered by Cognero Page 15
16 CHECK: 69. no solution esolutions Manual - Powered by Cognero Page 16
17 Solve each inequality. Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. 74. PHYSICS The formula represents the Now, solve. swing of a pendulum, where t is the time in seconds for the pendulum to swing back and forth and is the length of the pendulum in feet. Find the length of a pendulum that makes one swing in 2.75 seconds. Substitute 2.75 for t in the formula and solve. The solution region is. The length of a pendulum is about 6.13 ft. esolutions Manual - Powered by Cognero Page 17
18 Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. Now, solve. Now, solve. The solution region is The solution region is. esolutions Manual - Powered by Cognero Page 18
19 Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. Now, solve. Now, solve. The solution region is. Since there is no common region between the inequalities, the inequality has no solution. esolutions Manual - Powered by Cognero Page 19
20 80. Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined. Now, solve. The solution region is. 81. esolutions Manual - Powered by Cognero Page 20
2-6 Nonlinear Inequalities
31. Find the domain of each expression. For the expression to be defined, x 2 3x 40 0. Let f (x) = x 2 3x 40. A factored form of f (x) is f (x) = (x 8)(x + 5). f (x) has real zeros at x = 8 and x = 5.
SOLUTION: The domain of a square root function only includes values for which the radicand is nonnegative.
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 23.
6-7 Solving Radical Equations and Inequalities. Solve each equation. ANSWER: 20 ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: 10.
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
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.
Radical Equations and Inequalities
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7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. ANSWER: a 3 b 2 c 9.
2. Simplify each expression. Assume that no denominator equals zero. a 3 b 2 c 9 4. c 3 f 3 6. r 4 8. 10. nq 2 w 5 12. 1 14. 2rt 2 esolutions Manual - Powered by Cognero Page 1 16. 18. FINANCIAL LITERACY
Practice Test - Chapter Evaluate if x = 3 and y = 1. SOLUTION: 2. Simplify. SOLUTION:
1. Evaluate if x = 3 and y = 1. 2. Simplify. 3. MULTIPLE CHOICE If what is the value of A 105 B 9 C D 6 Substitute m = 6 in 2m 3. So, the correct choice is B. esolutions Manual - Powered by Cognero Page
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Find the area of each figure. 1. The area of the rectangle is 6 square centimeters. 2. The area of the square is 36 square inches. 3. The area of the parallelogram is 120 square meters. esolutions Manual
10-2 Simplifying Radical Expressions. Simplify each expression. SOLUTION: 4. SOLUTION: SOLUTION: SOLUTION: 10. MULTIPLE CHOICE Which expression is
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
Using the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
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[1] [2.3 b,c] [2] [2.3b] 3. Solve for x: 3x 4 2x. [3] [2.7 c] [4] [2.7 d] 5. Solve for h : [5] [2.4 b] 6. Solve for k: 3 x = 4k
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2-2 Linear Relations and Functions. State whether each function is a linear function. Write yes or no. Explain. ANSWER: Yes; it can be written as
1. 2. 3. 4. State whether each function is a linear function. Write yes or no. Explain. Yes; it can be written as No; it cannot be written as f (x) = mx + b. No; x has an exponent that is not 1. Yes; it
3C Histograms. Sample answer: The least value in the data is 1 and the greatest is 1,135. An interval of 200 would yield the frequency table below.
POPULATION The list gives the approximate population density for each state. Choose intervals and make a frequency table. Then construct a histogram to represent the data. Sample answer: The least value
3. If a coordinate is zero the point must be on an axis. If the x-coordinate is zero, where will the point be?
Chapter 2: Equations and Inequalities Section 1: The Rectangular Coordinate Systems and Graphs 1. Cartesian Coordinate System. 2. Plot the points ( 3, 5), (4, 3), (3, 4), ( 3, 0) 3. If a coordinate is
1-4 Extrema and Average Rates of Change
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Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals
Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive
1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =
Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is
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Determine whether the given lengths can be side lengths of a right triangle. 1. 6, 7, , 15, , 4, 5
Algebra Test Review Name Instructor Hr/Blk Determine whether the given lengths can be side lengths of a right triangle. 1., 7, 8. 17, 1, 8.,, For the values given, a and b are legs of a right triangle.
2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY
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7 2? 7 2 THE ANSWER KEY IS AT THE END OF THE PACKET. TOPIC: Rationalizing Denominators. 1. Which expression is equivalent to (3) (1) 9 5
NAME: Algebra /Trig Midterm POW #Review Packet #4 DATE: PERIOD: THE ANSWER KEY IS AT THE END OF THE PACKET 1. Which expression is equivalent to TOPIC: Rationalizing Denominators 7? 7 (1) 9 5 (3) 9 14 5
due Thursday, August 25, Friday, September 2, 2016 test Prerequisite Skills for Algebra II Advanced
Name: Student ID: Algebra II Advanced is a very rigorous and fast-paced course. In order to prepare for the rigor of this course, you will need to be familiar with the topics in this packet prior to starting
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Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved.
A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle
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Solve the equation in questions 1-4. 1. 7 x + 5 = 8 a. 7 b. 1 7 c. 7 d. 7. 7 = d + 0 a. 10 b. 0 c. 1 d. 1. p 1 = 5(p 1) (7 p) a. b. 0 c. 9 d. 10 4. 5x 5 = x 9 a. b. 1 c. 1 d. 5. A customer went to a garden
Practice Test - Chapter 2
1 State the domain and range of the relation shown in the table Then determine if it is a function If it is a function, determine if it is one-to-one, onto, both, or neither 4 Write 2y = 6x + 4 in standard
due test Prerequisite Skills for Algebra II Advanced
Name: Student ID: Algebra II Advanced is a very rigorous and fast-paced course. In order to prepare for the rigor of this course, you will need to be familiar with the topics in this packet prior to starting
The point is located eight units to the right of the y-axis and two units above the x-axis. A) ( 8, 2) B) (8, 2) C) ( 2, 8) D) (2, 8) E) ( 2, 8)
Name: Date: 1. Find the coordinates of the point. The point is located eight units to the right of the y-axis and two units above the x-axis. A) ( 8, ) B) (8, ) C) (, 8) D) (, 8) E) (, 8). Find the coordinates
2-4 Zeros of Polynomial Functions
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1-7 Compute with Scientific Notation
Evaluate each expression. Express the result in scientific notation. 1. (3.9 10 2 )(2.3 10 6 ) Use the Commutative and Associative Properties to group the factors and powers of 10. Multiply 3.9 and 2.3.
5-3 Solving Multi-Step Inequalities. Solve each inequality. Graph the solution on a number line b 1 11 SOLUTION: The solution set is {b b 2}.
Solve each inequality. Graph the solution on a number line. 12. 5b 1 11 14. 9 m + 7 The solution set is {b b 2}. {b b 2} The solution set is {m m 40}. 13. 21 > 15 + 2a {m m 40} 15. 13 > 6 The solution
Practice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. 1. An acute angle measure and the length of the hypotenuse are given, so the sine function can be used to find the length of the side opposite.
Study Guide and Review - Chapter 7
Choose a word or term from the list above that best completes each statement or phrase. 1. A function of the form f (x) = b x where b > 1 is a(n) function. exponential growth 2. In x = b y, the variable
Mid-Chapter Quiz: Lessons 1-1 through 1-4
Determine whether each relation represents y as a function of x. 1. 3x + 7y = 21 This equation represents y as a function of x, because for every x-value there is exactly one corresponding y-value. function
Simplifying Radicals. multiplication and division properties of square roots. Property Multiplication Property of Square Roots
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Simplify. 1. i 10 2. i 2 + i 8 3. i 3 + i 20 4. i 100 5. i 77 esolutions Manual - Powered by Cognero Page 1 6. i 4 + i 12 7. i 5 + i 9 8. i 18 Simplify. 9. (3 + 2i) + ( 4 + 6i) 10. (7 4i) + (2 3i) 11.
0-2 Operations with Complex Numbers
Simplify. 1. i 10 1 2. i 2 + i 8 0 3. i 3 + i 20 1 i esolutions Manual - Powered by Cognero Page 1 4. i 100 1 5. i 77 i 6. i 4 + i 12 2 7. i 5 + i 9 2i esolutions Manual - Powered by Cognero Page 2 8.
Solutions Key Exponential and Radical Functions
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5-7 Roots and Zeros. Solve each equation. State the number and type of roots. 1. x 2 3x 10 = 0 ANSWER: 2, 5; 2 real
Solve each equation. State the number and type of roots. 1. x 2 3x 10 = 0 2, 5; 2 real 2. x 3 + 12x 2 + 32x =0 8, 4, 0; 3 real 3. 16x 4 81 = 0 2 real, 2 imaginary 4. 0 = x 3 8 1 real, 2 imaginary State
1. Simplify by performing the indicated operation: (4 + 8i)(8 + i).
WSU CE Math 1010 REAL Final Review Read each question carefully and show all your work to receive full credit for your answers. The use of a scientific calculator is allowed. 1. Simplify by performing