Each element of the domain is paired with exactly one element of the range. So, the relation is a function.

Size: px
Start display at page:

Download "Each element of the domain is paired with exactly one element of the range. So, the relation is a function."

Transcription

1 CCSS STRUCTURE State the domain and range of each relation. Then determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. 1. The left side of the mapping is the domain and the right side is the range.the members of the domain are the x-values of the relation while the members of the range are the y-values. D = { 2, 5, 6}, R = { 8, 1, 3}; Each element of the domain is paired with exactly one element of the range. So, the relation is a function. The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range corresponds to an element of the domain. 2. D = { 2, 1, 4}, R = { 1, 2, 3, 5}; The relation is not a function because 1 is mapped to both 2 and D = { 2, 1, 4, 8}, R = { 4, 2, 6}; Each element of the domain is paired with exactly one element of the range. So, the relation is a function. The function is onto because each element of the range corresponds to an element of the domain. esolutions Manual - Powered by Cognero Page 1

2 4. BASKETBALL The table shows the average points per game for Dwayne Wade of the Miami Heat for four years. a. Assume that the ages are the domain. Identify the domain and range. b. Write a relation of ordered pairs for the data. c. State whether the relation is discrete or continuous. d. Graph the relation. Is this relation a function? a. Since the ages are the domain, the average points per game are the range. D = {24, 25, 26, 27}, R = {24.6, 27.2, 27.4, 30.2} b. In writing ordered pairs for the relation, the members of the domain are the x-values and the members of the range are the y-values. {(24, 27.2), (25, 27.4), (26, 24.6), (27, 30.2)} c. The domain is a set of individual points. So the relation is discrete. d. The relation is a function as each element of the domain is paired with exactly one element of the range. esolutions Manual - Powered by Cognero Page 2

3 5. Graph each equation, and determine the domain and range. Determine whether the equation is a function, is one-to-one, onto, both, or neither. Then state whether it is discrete or continuous. To graph the equation, substitute different values of x in the equation and solve for y. Then connect the points. x y = 5x D = {all real numbers}; R = {all real numbers}; No vertical line intersects the graph in more than one point. So the graph is a function. The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range corresponds to an element of the domain. The graph of the function is a line. So the function is continuous. esolutions Manual - Powered by Cognero Page 3

4 6. To graph the equation, substitute different values of x in the equation and solve for y. Then connect the points. x y = -4x D = {all real numbers}; R = {all real numbers}; No vertical line intersects the graph in more than one point. So the graph is a function. The function is both one-to-one and onto because each element of the domain is paired with a unique element of the range and each element of the range correspond to an element of the domain. The domain has an infinite number of elements and the relation can be graphed using a straight line. So the relation is continuous. esolutions Manual - Powered by Cognero Page 4

5 7. To graph the equation, substitute different values of x in the equation and solve for y. Then connect the points. x y = 3x D = {all real numbers}; R = {all real numbers}; No vertical line intersects the graph in more than one point. So the graph is a function. The function is neither one-to-one nor onto because the elements in the domain do not have unique images and the negative numbers are left unmapped. The domain has an infinite number of elements and the relation can be graphed using a smooth curve. So the relation is continuous. esolutions Manual - Powered by Cognero Page 5

6 8. The graph of the equation is a vertical line through (7, 0). In this equation x is always 7 for any value of y. D = {7}; R = {all real numbers}; The only element in the domain is mapped to all the elements in the range. So it is not a function. The domain has a finite number (1) of elements, so the relation is not continuous. esolutions Manual - Powered by Cognero Page 6

2-1 Relations and Functions

2-1 Relations and Functions CCSS STRUCTURE State the domain and range of each relation. Then determine whether each relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. 4. BASKETBALL

More information

Mid-Chapter Quiz: Lessons 1-1 through 1-4

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

More information

Practice Test - Chapter 2

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

More information

10-1 Sequences as Functions. Determine whether each sequence is arithmetic. Write yes or no , 3, 0, 3, 9

10-1 Sequences as Functions. Determine whether each sequence is arithmetic. Write yes or no , 3, 0, 3, 9 Determine whether each sequence is arithmetic. Write yes or no. 22. 9, 3, 0, 3, 9 Find the next four terms of each arithmetic sequence. Then graph the sequence. 26. 10, 2, 6, 14, There is no common difference.

More information

1-1 Functions < x 64 SOLUTION: 9. { 0.25, 0, 0.25, 0.50, } SOLUTION: 12. all multiples of 8 SOLUTION: SOLUTION:

1-1 Functions < x 64 SOLUTION: 9. { 0.25, 0, 0.25, 0.50, } SOLUTION: 12. all multiples of 8 SOLUTION: SOLUTION: Write each set of numbers in set-builder and interval notation, if possible. 3. x 4 The set includes all real numbers less than or equal to 4. In set-builder notation this set can be described as {x x

More information

10-1 Sequences as Functions. Determine whether each sequence is arithmetic. Write yes or no. 1. 8, 2, 12, 22

10-1 Sequences as Functions. Determine whether each sequence is arithmetic. Write yes or no. 1. 8, 2, 12, 22 Determine whether each sequence is arithmetic. Write yes or no. 1. 8, 2, 12, 22 Subtract each term from the term directly after it. The common difference is 10. 3. 1, 2, 4, 8, 16 Subtract each term from

More information

1-6 Ordered Pairs and Relations

1-6 Ordered Pairs and Relations Graph each ordered pair on a coordinate plane. 2. A(2, 5) Start at the origin. The x-coordinate is 2, so move 2 units to the right. The y-coordinate is 5, so move 5 units up. Draw a dot, and label it A.

More information

6-2 Matrix Multiplication, Inverses and Determinants

6-2 Matrix Multiplication, Inverses and Determinants Find AB and BA, if possible. 1. A = A = ; A is a 1 2 matrix and B is a 2 2 matrix. Because the number of columns of A is equal to the number of rows of B, AB exists. To find the first entry of AB, find

More information

4-7 Inverse Linear Functions

4-7 Inverse Linear Functions Find the inverse of each relation. 1. {(4, 15), ( 8, 18), ( 2, 16.5), (3, 15.25)} {( 15, 4), ( 18, 8), ( 16.5, 2), ( 15.25, 3)} 2. {(11.8, 3), (3.7, 0), (1, 1), ( 12.5, 6)} Graph the inverse of each relation.

More information

Find (f + g )(x), (f g)(x), (x),and (x) for each f (x) and g(x). Indicate any restrictions in

Find (f + g )(x), (f g)(x), (x),and (x) for each f (x) and g(x). Indicate any restrictions in Find (f + g )(x), (f g)(x), (x),and (x) for each f (x) and g(x). Indicate any restrictions in domain or range. 2. esolutions Manual - Powered by Cognero Page 1 For each pair of functions, find and, if

More information

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}.

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

More information

Practice Test - Chapter 2

Practice Test - Chapter 2 Graph and analyze each function. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing. 1. f (x) = 0.25x 3 Evaluate the function for several

More information

7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. ANSWER: a 3 b 2 c 9.

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

More information

2-4 Zeros of Polynomial Functions

2-4 Zeros of Polynomial Functions Write a polynomial function of least degree with real coefficients in standard form that has the given zeros. 33. 2, 4, 3, 5 Using the Linear Factorization Theorem and the zeros 2, 4, 3, and 5, write f

More information

Plot the points on the coordinate plane and connect them by a smooth curve.

Plot the points on the coordinate plane and connect them by a smooth curve. Graph each polynomial equation by making a table of values. 2. f (x) = 2x 4 + 4x 3 + 2x 2 + x 3 Make a table of values. Plot the points on the coordinate plane and connect them by a smooth curve. esolutions

More information

The function is defined for all values of x. Therefore, the domain is set of all real numbers.

The function is defined for all values of x. Therefore, the domain is set of all real numbers. Graph each function. State the domain and range. 1. f (x) = 3 x 3 + 2 The function is defined for all values of x. Therefore, the domain is set of all real numbers. The value of f (x) tends to 2 as x tends

More information

2-6 Algebraic Proof. State the property that justifies each statement. 1. If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. SOLUTION:

2-6 Algebraic Proof. State the property that justifies each statement. 1. If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. SOLUTION: State the property that justifies each 1. If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. There are two parts to the hypotheses. "If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. "The end of the first part of the

More information

6-3 Square Root Functions and Inequalities. Identify the domain and range of each function. ANSWER: ANSWER:

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.

More information

Given a polynomial and one of its factors, find the remaining factors of the polynomial. 4. x 3 6x x 6; x 1 SOLUTION: Divide by x 1.

Given a polynomial and one of its factors, find the remaining factors of the polynomial. 4. x 3 6x x 6; x 1 SOLUTION: Divide by x 1. Use synthetic substitution to find f (4) and f ( 2) for each function. 2. f (x) = x 4 + 8x 3 + x 2 4x 10 Divide the function by x 4. The remainder is 758. Therefore, f (4) = 758. Divide the function by

More information

9-5 Complex Numbers and De Moivre's Theorem

9-5 Complex Numbers and De Moivre's Theorem Find each power and express it in rectangular form. 37. (12i 5) 3 First, write 12i 5 in polar form. The polar form of 12i 5 is. Now use De Moivre s Theorem to find the third power. Therefore,. esolutions

More information

the number of cars passing through an intersection in a given time interval

the number of cars passing through an intersection in a given time interval Identify the random variable in each distribution, and classify it as discrete or continuous. Explain your reasoning. the number of stations in a cable package The random variable X is the number of stations

More information

3-3 Complex Numbers. Simplify. SOLUTION: 2. SOLUTION: 3. (4i)( 3i) SOLUTION: 4. SOLUTION: 5. SOLUTION: esolutions Manual - Powered by Cognero Page 1

3-3 Complex Numbers. Simplify. SOLUTION: 2. SOLUTION: 3. (4i)( 3i) SOLUTION: 4. SOLUTION: 5. SOLUTION: esolutions Manual - Powered by Cognero Page 1 1. Simplify. 2. 3. (4i)( 3i) 4. 5. esolutions Manual - Powered by Cognero Page 1 6. 7. Solve each equation. 8. Find the values of a and b that make each equation true. 9. 3a + (4b + 2)i = 9 6i Set the

More information

Practice Test - Chapter 3

Practice Test - Chapter 3 Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing. 1. f (x) = e x + 7 Evaluate the function

More information

8. 2 3x 1 = 16 is an example of a(n). SOLUTION: An equation in which the variable occurs as exponent is an exponential equation.

8. 2 3x 1 = 16 is an example of a(n). SOLUTION: An equation in which the variable occurs as exponent is an exponential equation. Choose the word or term that best completes each sentence. 1. 7xy 4 is an example of a(n). A product of a number and variables is a monomial. 2. The of 95,234 is 10 5. 95,234 is almost 100,000 or 10 5,

More information

1-4 Extrema and Average Rates of Change

1-4 Extrema and Average Rates of Change Use the graph of each function to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically. 6. 3. When the graph is viewed

More information

10-2 Arithmetic Sequences and Series

10-2 Arithmetic Sequences and Series Determine the common difference, and find the next four terms of each arithmetic sequence. 1. 20, 17, 14, 17 20 = 3 14 17 = 3 The common difference is 3. Add 3 to the third term to find the fourth term,

More information

Study Guide and Review - Chapter 2. Choose the correct term to complete each sentence.

Study Guide and Review - Chapter 2. Choose the correct term to complete each sentence. Choose the correct term to complete each sentence 1 A function is (discrete, one-to-one) if each element of the domain is paired to exactly one unique element of the range one-to-one 2 The (domain, range)

More information

8-3 Dot Products and Vector Projections

8-3 Dot Products and Vector Projections Find the dot product of u and v. Then determine if u and v are orthogonal. 3. u = 9, 3, v = 1, 3 Since, u and v are orthogonal. 6. u = 11i + 7j; v = 7i + 11j Write u and v in component form as Since, u

More information

Study Guide and Review - Chapter 5. Solve each inequality. Then graph it on a number line. 11. w 4 > 9 SOLUTION: The solution set is {w w > 13}.

Study Guide and Review - Chapter 5. Solve each inequality. Then graph it on a number line. 11. w 4 > 9 SOLUTION: The solution set is {w w > 13}. Solve each inequality. Then graph it on a number line. 11. w 4 > 9 The solution set is {w w > 13}. 13. 6 + h < 1 The solution set is {h h < 5}. 15. 13 p 15 The solution set is {p p 2}. 17. FIELD TRIP A

More information

3-4 Systems of Equations in Three Variables. Solve each system of equations. SOLUTION:

3-4 Systems of Equations in Three Variables. Solve each system of equations. SOLUTION: Solve each system of equations. 3. Multiply the second equation by 2 and add with the third equation. Multiply the first equation by 2 and add with the second equation. Solve the fifth and fourth equations.

More information

10-2 Arithmetic Sequences and Series. Write an equation for the nth term of each arithmetic sequence. 29. SOLUTION: to find the nth term.

10-2 Arithmetic Sequences and Series. Write an equation for the nth term of each arithmetic sequence. 29. SOLUTION: to find the nth term. 29 Write an equation for the nth term of each arithmetic sequence 32 CCSS STRUCTURE José averaged 123 total pins per game in his bowing league this season He is taking bowling lessons and hopes to bring

More information

13-5 Probabilities of Independent and Dependent Events

13-5 Probabilities of Independent and Dependent Events CCSS REASONING Determine whether the events are independent or dependent. Then find the probability. 6. In a game, you roll an even number on a die and then spin a spinner numbered 1 through 5 and get

More information

Mid-Chapter Quiz: Lessons 2-1 through 2-3

Mid-Chapter Quiz: Lessons 2-1 through 2-3 Graph and analyze each function. Describe its domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing. 1. f (x) = 2x 3 Evaluate the function for several

More information

4-8 Quadratic Inequalities. Graph each inequality. ANSWER: ANSWER: ANSWER: CCSS SENSE-MAKING Solve each inequality by graphing.

4-8 Quadratic Inequalities. Graph each inequality. ANSWER: ANSWER: ANSWER: CCSS SENSE-MAKING Solve each inequality by graphing. 1. Graph each inequality. 4. CCSS SENSE-MAKING Solve each inequality by graphing. {x x < 1 or x > 4} 5. {x 5 < x < 3} 2. 6. {x 3 x 2} 7. {x 0.29 x 1.71} 3. 8. SOCCER A midfielder kicks a ball toward the

More information

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

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

More information

5-5 The Triangle Inequality

5-5 The Triangle Inequality Is it possible to form a triangle with the given side lengths? If not, explain why not. 1. 5 cm, 7 cm, 10 cm Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5 3. 6 m, 14 m, 10 m Yes; 6 + 14 > 10, 6 + 10 > 14,

More information

2-3 The Remainder and Factor Theorems

2-3 The Remainder and Factor Theorems Factor each polynomial completely using the given factor and long division. 3. x 3 + 3x 2 18x 40; x 4 So, x 3 + 3x 2 18x 40 = (x 4)(x 2 + 7x + 10). Factoring the quadratic expression yields x 3 + 3x 2

More information

scatter plot Study Guide and Review - Chapter 2 Choose the correct term to complete each sentence.

scatter plot Study Guide and Review - Chapter 2 Choose the correct term to complete each sentence. Choose the correct term to complete each sentence. 1. A function is (discrete, one-to-one) if each element of the domain is paired to exactly one unique element of the range. one-to-one 2. The (domain,

More information

0-2 Operations with Complex Numbers

0-2 Operations with Complex Numbers 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.

More information

0-2 Operations with Complex Numbers

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.

More information

Practice Test - Chapter 2

Practice Test - Chapter 2 Graph and analyze each function. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing. 1. f (x) = 0.25x 3 Evaluate the function for several

More information

SOLUTION: The domain of a square root function only includes values for which the radicand is nonnegative.

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.

More information

Study Guide and Review - Chapter 6

Study Guide and Review - Chapter 6 State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. If a system has at least one solution, it is said to be consistent. Graph each system and determine

More information

3-5 Solving Systems of Equations Using Cramer's Rule. Evaluate each determinant. ANSWER: 26 ANSWER: 128. Evaluate each determinant using diagonals.

3-5 Solving Systems of Equations Using Cramer's Rule. Evaluate each determinant. ANSWER: 26 ANSWER: 128. Evaluate each determinant using diagonals. 1. 3. 5. Evaluate each determinant. 26 128 Evaluate each determinant using diagonals. 13. 4x 5y = 39 3x + 8y = 6 (6, 3) 15. 8a 5b = 27 7a + 6b = 22 (4, 1) 17. CCSS PERSEVERANCE The Bermuda Triangle is

More information

3-1 Constant Rate of Change

3-1 Constant Rate of Change Determine whether the relationship between the two quantities shown in the table or graph is linear. If so, find the constant rate of change. If not, explain your reasoning. 1. Analyze the table. The rate

More information

3-4 Equations of Lines

3-4 Equations of Lines Write an equation in slope-intercept form of the line having the given slope and y-intercept. Then graph the line. 1. m: 4, y-intercept: 3 3. y-intercept: 5 y = 4x 3 2. y-intercept: 1 Write an equation

More information

Study Guide and Review - Chapter 12

Study Guide and Review - Chapter 12 Choose the correct term to complete each sentence. 1. The slope of a nonlinear graph at a specific point is the and can be represented by the slope of the tangent line to the graph at that point. The slope

More information

1-2 Analyzing Graphs of Functions and Relations

1-2 Analyzing Graphs of Functions and Relations Use the graph of each function to estimate the indicated function values. Then confirm the estimate algebraically. Round to the nearest hundredth, if necessary. 2. 6. a. h( 1) b. h(1.5) c. h(2) a. g( 2)

More information

10-2 Simplifying Radical Expressions. Simplify each expression. SOLUTION: 4. SOLUTION: SOLUTION: SOLUTION: 10. MULTIPLE CHOICE Which expression is

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

More information

2-6 Analyzing Functions with Successive Differences

2-6 Analyzing Functions with Successive Differences Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. 1. ( 2, 8), ( 1, 5), (0, 2), (1, 1) linear 3. ( 3, 8),

More information

1-1 Functions. 3. x 4 SOLUTION: 5. 8 < x < 99 SOLUTION: 7. x < 19 or x > 21 SOLUTION: 9. { 0.25, 0, 0.25, 0.50, } SOLUTION:

1-1 Functions. 3. x 4 SOLUTION: 5. 8 < x < 99 SOLUTION: 7. x < 19 or x > 21 SOLUTION: 9. { 0.25, 0, 0.25, 0.50, } SOLUTION: 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,

More information

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.

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

More information

7-2 Solving Exponential Equations and Inequalities

7-2 Solving Exponential Equations and Inequalities Write an exponential function for the graph that passes through the given points. 16. (0, 6.4) and (3, 100) Substitute 100 for y and 6.4 for a and 3 for x into an exponential function and determine the

More information

2-5 Rational Functions

2-5 Rational Functions 19. SALES The business plan for a new car wash projects that profits in thousands of dollars will be modeled by the function p (z) =, where z is the week of operation and z = 0 represents opening. a. State

More information

Study Guide and Review -Chapter 1

Study Guide and Review -Chapter 1 State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. An exponent indicates the number the base is to be multiplied by. True 2. A coordinate system is formed

More information

Definition: A "system" of equations is a set or collection of equations that you deal with all together at once.

Definition: A system of equations is a set or collection of equations that you deal with all together at once. System of Equations Definition: A "system" of equations is a set or collection of equations that you deal with all together at once. There is both an x and y value that needs to be solved for Systems

More information

2-4 Zeros of Polynomial Functions

2-4 Zeros of Polynomial Functions List all possible rational zeros of each function Then determine which, if any, are zeros 1 g(x) = x 4 6x 3 31x 2 + 216x 180 Because the leading coefficient is 1, the possible rational zeros are the integer

More information

7-6 Growth and Decay. Let t = 7 in the salary equation above. So, Ms. Acosta will earn about $37, in 7 years.

7-6 Growth and Decay. Let t = 7 in the salary equation above. So, Ms. Acosta will earn about $37, in 7 years. 1. SALARY Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in

More information

4-3 Trigonometric Functions on the Unit Circle

4-3 Trigonometric Functions on the Unit Circle Find the exact value of each trigonometric function, if defined. If not defined, write undefined. 9. sin The terminal side of in standard position lies on the positive y-axis. Choose a point P(0, 1) on

More information

9-4 Ellipses. Write an equation of each ellipse. 1. ANSWER: ANSWER:

9-4 Ellipses. Write an equation of each ellipse. 1. ANSWER: ANSWER: Write an equation of each ellipse. 5. CCSS SENSE-MAKING An architectural firm sent a proposal to a city for building a coliseum, shown at the right. 1. a. Determine the values of a and b. b. Assuming that

More information

2-4 Solving Equations with the Variable on Each Side. Solve each equation. Check your solution x + 2 = 4x + 38 ANSWER: 4 ANSWER:

2-4 Solving Equations with the Variable on Each Side. Solve each equation. Check your solution x + 2 = 4x + 38 ANSWER: 4 ANSWER: 1. 13x + 2 = x + 38 9. MULTIPLE CHOICE Find the value of x so that t figures have the same perimeter. 2. 3. 6(n + ) = 18 7. 7 = 11 + 3(b + 5) 1 5. 5 + 2(n + 1) = 2n 6. 7 3r = r (2 + r) 7. 1v + 6 = 2(5

More information

Study Guide and Review. 11. Find EG if G is the incenter of.

Study Guide and Review. 11. Find EG if G is the incenter of. 11. Find EG if G is the incenter of. By the Incenter Theorem, since G is equidistant from the sides of Pythagorean Theorem., EG = FG. Find FG using the Since length cannot be negative, use only the positive

More information

Solve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6 ANSWER: 5.2, 1.2

Solve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6 ANSWER: 5.2, 1.2 Find the value of c that makes each trinomial a perfect square. 1. x 2 18x + c 81 3. x 2 + 9x + c Solve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6

More information

5-3 Polynomial Functions

5-3 Polynomial Functions State the degree and leading coefficient of each polynomial in one variable. If it is not a polynomial in one variable, explain why. 1. 11x 6 5x 5 + 4x 2 degree = 6, leading coefficient = 11 2. 10x 7 5x

More information

12-4 Law of Sines. Find the area of ABC to the nearest tenth, if necessary. SOLUTION: Substitute c = 7, b = 8 and A = 86º in the area. formula.

12-4 Law of Sines. Find the area of ABC to the nearest tenth, if necessary. SOLUTION: Substitute c = 7, b = 8 and A = 86º in the area. formula. Find the area of ABC to the nearest tenth, if necessary. 3. A = 40, b = 11 cm, c = 6 cm Substitute c = 6, b = 11 and A = 40º in the area 1. Substitute c = 7, b = 8 and A = 86º in the area 4. B = 103, a

More information

2-6 Nonlinear Inequalities

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.

More information

7-2 Similar Polygons. CCSS REGULARITY Each pair of polygons is similar. Find the value of x.

7-2 Similar Polygons. CCSS REGULARITY Each pair of polygons is similar. Find the value of x. CCSS REGULARITY Each pair of polygons is similar. Find the value of x. 18. Solve for x. 19. Solve for x. esolutions Manual - Powered by Cognero Page 1 20. Solve for x. 21. Solve for x. esolutions Manual

More information

8-2 Adding and Subtracting Rational Expressions. Find the LCM of each set of polynomials x, 8x 2 y 3, 5x 3 y.

8-2 Adding and Subtracting Rational Expressions. Find the LCM of each set of polynomials x, 8x 2 y 3, 5x 3 y. Find the LCM of each set of polynomials. 11. 1. 16x, 8x 2 y 3, 5x 3 y 80x 3 y 2 3. 3y 2 9y, y 2 8y + 15 13. GEOMETRY Find the perimeter of the rectangle. 3y(y 3)(y 5) 5. 15. 7. 9. 17. esolutions Manual

More information

7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. SOLUTION: SOLUTION: SOLUTION: SOLUTION:

7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. SOLUTION: SOLUTION: SOLUTION: SOLUTION: Simplify each expression. Assume that no denominator equals zero. 1. 2. 3. 4. Page 1 4. 5. 6. 7. Page 2 7. 8. 9. 10. Page 3 10. 11. 12. A value to the zero power is 1. 13. A value to the zero power is

More information

10-3 Geometric Sequences and Series

10-3 Geometric Sequences and Series 1. CCSS REGULARITY Dean is making a family tree for his grandfather. He was able to trace many generations. If Dean could trace his family back 10 generations, starting with his parents how many ancestors

More information

8-6 Solving Rational Equations and Inequalities. Solve each equation. Check your solution. ANSWER: 11 ANSWER: 9 ANSWER: 7 ANSWER: 3 ANSWER: 8

8-6 Solving Rational Equations and Inequalities. Solve each equation. Check your solution. ANSWER: 11 ANSWER: 9 ANSWER: 7 ANSWER: 3 ANSWER: 8 Solve each equation. Check your solution. 1. 11 2. 9 3. 7 4. 3 5. 8 6. 5 esolutions Manual - Powered by Cognero Page 1 7. 14 8. 14 9. CCSS STRUCTURE Sara has 10 pounds of dried fruit selling for $6.25

More information

4-6 Inverse Trigonometric Functions

4-6 Inverse Trigonometric Functions Find the exact value of each expression, if it exists 1 sin 1 0 with a y-coordinate of 0 3 arcsin When t = 0, sin t = 0 Therefore, sin 1 0 = 0 2 arcsin When t =, sin t = Therefore, arcsin = 4 sin 1 When

More information

1-3 Locating Points and Midpoints

1-3 Locating Points and Midpoints 13 APPLY MATH A business is trying to decide where to build an office The business wants to place the office halfway between city B and city C If city B is at (3, 9) and city C is at (3, 5), find the coordinates

More information

8-1 Multiplying and Dividing Rational Expressions. Simplify each expression. ANSWER: 3. MULTIPLE CHOICE Identify all values of x for which

8-1 Multiplying and Dividing Rational Expressions. Simplify each expression. ANSWER: 3. MULTIPLE CHOICE Identify all values of x for which 7. 1. 9. 3. MULTIPLE CHOICE Identify all values of x for which is undefined. A 7, 4 B 7, 4 C 4, 7, 7 11. D 4, 7 D 4 5. 13. 15. esolutions Manual - Powered by Cognero Page 1 17. 25. 19. MULTIPLE CHOICE

More information

9-3 Constant Rate of Change and Slope

9-3 Constant Rate of Change and Slope Find the constant rate of change between the quantities in each table. 5. Find the slope of the line in the graph below. 1. $2.40 per item 2. 20 ft per min Find the constant rate of change for each linear

More information

8-2 The Pythagorean Theorem and Its Converse. Find x. 27. SOLUTION: The triangle with the side lengths 9, 12, and x form a right triangle.

8-2 The Pythagorean Theorem and Its Converse. Find x. 27. SOLUTION: The triangle with the side lengths 9, 12, and x form a right triangle. Find x. 27. The triangle with the side lengths 9, 12, and x form a right triangle. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

More information

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

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

More information

5-6 The Remainder and Factor Theorems

5-6 The Remainder and Factor Theorems Use synthetic substitution to find f (4) and f ( 2) for each function. 1. f (x) = 2x 3 5x 2 x + 14 58; 20 2. f (x) = x 4 + 8x 3 + x 2 4x 10 758; 46 3. NATURE The approximate number of bald eagle nesting

More information

8-2 Vectors in the Coordinate Plane

8-2 Vectors in the Coordinate Plane 37. ROWING Nadia is rowing across a river at a speed of 5 miles per hour perpendicular to the shore. The river has a current of 3 miles per hour heading downstream. a. At what speed is she traveling? b.

More information

4-6 Inverse Trigonometric Functions

4-6 Inverse Trigonometric Functions Find the exact value of each expression, if it exists. 1. sin 1 0 0 2. arcsin 9. 10. cos 1 11. arctan 1 3. arcsin 4. sin 1 5. 12. arctan ( ) 13. 6. arccos 0 14. tan 1 0 0 15. ARCHITECTURE The support for

More information

Practice Test - Chapter Evaluate if x = 3 and y = 1. SOLUTION: 2. Simplify. SOLUTION:

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

More information

5-5 Inequalities Involving Absolute Value. Solve each inequality. Then graph the solution set. 1. a 5 < 3 ANSWER: {a 2 < a < 8} 2.

5-5 Inequalities Involving Absolute Value. Solve each inequality. Then graph the solution set. 1. a 5 < 3 ANSWER: {a 2 < a < 8} 2. Solve each inequality. Then graph the solution set. 1. a 5 < 3 {a 2 < a < 8} Solve each inequality. Then graph the solution set. 8. x + 8 < 16 {x 24 < x < 8} 2. u + 3 < 7 {u 10 < u < 4} 9. r + 1 2 {r 3

More information

7-6 Common Logarithms

7-6 Common Logarithms Use a calculator to evaluate each expression to the nearest ten-thousandth. 1. log 5 KEYSTROKES: LOG 5 ENTER 0.698970043 5. SCIENCE The amount of energy E in ergs that an earthquake releases is related

More information

7-1 Fractions and Percents

7-1 Fractions and Percents Write each percent as a fraction or mixed number in simplest form. 1. 40% 2. 14 % 3. 150% 4. 0.9% esolutions Manual - Powered by Cognero Page 1 5. Write each fraction as a percent. Round to the nearest

More information

3-1 Solving Systems of Equations. Solve each system of equations by using a table. 1. ANSWER: (3, 5) ANSWER: (2, 7)

3-1 Solving Systems of Equations. Solve each system of equations by using a table. 1. ANSWER: (3, 5) ANSWER: (2, 7) Solve each system of equations by using a table. 1. 9. CCSS MODELING Refer to the table below. (3, 5) 2. (2, 7) Solve each system of equations by graphing. 3. a. Write equations that represent the cost

More information

Practice Test - Chapter 4

Practice Test - Chapter 4 Find the value of x. Round to the nearest tenth, if necessary. Find the measure of angle θ. Round to the nearest degree, if necessary. 1. An acute angle measure and the length of the hypotenuse are given,

More information

Study Guide and Review - Chapter 6. Choose a word or term that best completes each statement.

Study Guide and Review - Chapter 6. Choose a word or term that best completes each statement. 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

More information

13-2 Verifying Trigonometric Identities. CCSS PRECISION Verify that each equation is an identity. ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER:

13-2 Verifying Trigonometric Identities. CCSS PRECISION Verify that each equation is an identity. ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: CCSS PRECISION Verify that each equation is an identity. 4.. 5. 2. 3. 6. 7. MULTIPLE CHOICE Which expression can be used to form an identity with? A. B. C. D. D esolutions Manual - Powered by Cognero Page

More information

9-3 Constant Rate of Change and Slope

9-3 Constant Rate of Change and Slope Find the constant rate of change between the quantities in each table. Find the constant rate of change for each linear function and interpret its meaning. 1. The cost increases by $12 for every 5 items.

More information

0-8 Area. Find the area of each figure. 1. SOLUTION: The area of the rectangle is 6 square centimeters. 2. SOLUTION:

0-8 Area. Find the area of each figure. 1. SOLUTION: The area of the rectangle is 6 square centimeters. 2. SOLUTION: 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

More information

Study Guide and Review - Chapter 7

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

More information

6-7 Solving Radical Equations and Inequalities. Solve each equation. ANSWER: 20 ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: 10.

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

More information

7-8 Using Exponential and Logarithmic Functions

7-8 Using Exponential and Logarithmic Functions 1. PALEONTOLOGY The half-life of Potassium-40 is about 1.25 billion years. a. Determine the value of k and the equation of decay for Potassium-40. b. A specimen currently contains 36 milligrams of Potassium-40.

More information

Chapter 6. Functions. 01/2017 LSowatsky 1

Chapter 6. Functions. 01/2017 LSowatsky 1 Chapter 6 Functions 01/2017 LSowatsky 1 6.1A Constant Rate of Change I can Identify proportional and nonproportional linear relationships by finding a constant rate of change CCSS 8.EE.5, 8.F.4 LSowatsky

More information

Inquiry Lab: Unit Rates

Inquiry Lab: Unit Rates Work with a partner to solve. 1. Travis drove 129 miles in 3 hours. He drove at a constant speed. How many miles did he drive in 1 hour? Step 1 The bar diagram represents 129 miles. Divide the bar diagram

More information

3-4 Exponential and Logarithmic Equations

3-4 Exponential and Logarithmic Equations Solve each equation. 39. 7 2x + 1 = 3 x + 3 41. 9 x + 2 = 2 5x 4 47. 2 5x + 6 = 4 2x + 1 49. ASTRONOMY The brightness of two celestial bodies as seen from Earth can be compared by determining the variation

More information

5-3 Solving Trigonometric Equations

5-3 Solving Trigonometric Equations Solve each equation for all values of x. 1. 5 sin x + 2 = sin x The period of sine is 2π, so you only need to find solutions on the interval. The solutions on this interval are and. Solutions on the interval

More information

4-6 The Quadratic Formula and the Discriminant. Solve each equation by using the Quadratic Formula. 1. ANSWER: ANSWER: ANSWER: ANSWER: ANSWER:

4-6 The Quadratic Formula and the Discriminant. Solve each equation by using the Quadratic Formula. 1. ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: Solve each equation by using the Quadratic Formula. 7. 1. 2. 8. 3. 9. CCSS MODELING An amusement park ride takes riders to the top of a tower and drops them at speeds reaching 80 feet per second. A function

More information

8-1 Geometric Mean. SOLUTION: We have the diagram as shown.

8-1 Geometric Mean. SOLUTION: We have the diagram as shown. 25. CCSS MODELING Makayla is using a book to sight the top of a waterfall. Her eye level is 5 feet from the ground and she is a horizontal distance of 28 feet from the waterfall. Find the height of the

More information

and 5-4 Solving Compound Inequalities Solve each compound inequality. Then graph the solution set. p 8 and p

and 5-4 Solving Compound Inequalities Solve each compound inequality. Then graph the solution set. p 8 and p Solve each compound inequality. Then graph the solution set. p 8 and p and The solution set is {p p To graph the solution set, graph p and graph p. Then find the intersection. r + 6 < 8 or r 3 > 10 or

More information