Algebra 2 B - Unit 3: Rational Functions

(3.6) Solving Rational Equations Quiz Part 2- Quiz (1-2) 2. Simplify the sum. State any restrictions on the variables. (3 points) x-2/x+3 + 10x/x²-9

((x-2)(x-3) + 10x) / [(x-3) (x+3)] (x^2 - 5x + 6 + 10x) / [(x-3) (x+3)] (x^2 + 5x + 6) / [(x-3) (x+3)] [(x+3) (x+2)] / [(x-3) (x+3)] (x+2) / (x-3) There is a hole on x = -3. There is a restriction that x ≠3, -3. 3/3 points The final score is 6/6 (100%). (That is if you put those answers.)

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 6. Simplify the difference. (1 point) a^2-2a-3/a^2-9a+18 - a^2-5a-6/a^2+9a+8 A. 21a-28/(a-6)(a+8) B. 2a²-28/(a-6)(a+8) C. -3a+44/(a-6)(a+8) D. 2a²+18a+44/2a²+44

A. 21a-28/(a-6)(a+8) 1/1 point

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 5. Simplify the sum. (1 point) 7/a+8 + 7/a²-64 A. 7a-49/(a-8)(a+8) B. 14/a²+a-56 C. 14/(a-8)(a+8) D. 7a+63/(a-8)(a+8)

A. 7a-49/(a-8)(a+8) 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 7. Find the sum. (1 point) 4/x²-9 + 7/x+3 A. 7x-17/(x+3)×(x-3) B. 7x-17/(x+3)×(x+3) C. 11/x²+x-9 D. 7x-17/(x-3)²

A. 7x-17/(x+3)×(x-3) 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 9. What is the graph of the rational function? y=-3x+5/-5x+2 A. The graph is on google docs. B. The graph is on google docs. C. The graph is on google docs. D. The graph is on google docs. (Graphs are on google docs. Go to https://docs.google.com/document/d/19jW7945oXX8vLzAUEespVdVIIASra68BXCYZYxtwKqo/edit?usp=sharing to get the graphs)

A. The graph is on google docs 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 4. Find the difference. (1 point) x/25x-125 - 1/x²-5x A. x+5/25x B. x+5/25x(x-5) C. x-5/25x D. (x+5)(x-5)/25x

A. x+5/25x 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 3. Find the sum. (1 point) 5y+2/xy² + 2x-4/4xy A. xy+8y+4/2xy² B. 5y+2x-2/2xy² C. 5y+2x-2/xy² D. xy+8y+4/4xy²

A. xy+8y+4/2xy² 1/1 point

(3.7) Rational Functions Practice Practice (1-10) 1. Suppose that y varies inversely with w and x, inversely with z, and suppose that y=360, when w =8, x=15, and z =3. Write the equation that models this relationship (1 point) A. y=9wx/z B. y=z/9wx C. y=wx/9z D. y=9z/wx

A. y=9wx/z 1/1 point

(3.1) Do you think you're ready to start the lesson?- Skills Check (1-1) 1. Do you think you are ready to start the lesson? Choose the option that best describes how comfortable you are with the skills on this slide. (1 point) A. I understand these skills and I can explain them to others. I am ready to start the lesson. B. I generally understand these skills. I am ready to start the lesson. C. I understand these skills when I have help. I should practice more before I start the lesson. D. I do not understand these skills. I need more practice before I start the lesson.

All of the answer choices are correct so it wouldn't matter which one you choice but choose whichever one is true for you. The teachers would want you to put A but don't put A if you cant do A. 1/1 point The final score is 1/1 (100%). The final adjusted score is 1/1 (100%). (That is if you put that answers.)

(3.2) Do you think you're ready to start the lesson?- Skills Check (1-1) 1. Do you think you are ready to start the lesson? Choose the option that best describes how comfortable you are with the skills on this slide. (1 point) A. I understand these skills and I can explain them to others. I am ready to start the lesson. B. I generally understand these skills. I am ready to start the lesson. C. I understand these skills when I have help. I should practice more before I start the lesson. D. I do not understand these skills. I need more practice before I start the lesson.

All of the answer choices are correct so it wouldn't matter which one you choice but choose whichever one is true for you. The teachers would want you to put A but don't put A if you cant do A. 1/1 point The final score is 1/1 (100%). The final adjusted score is 1/1 (100%). (That is if you put that answers.)

(3.3) Do you think you're ready to start the lesson?- Skills Check (1-1) 1. Do you think you are ready to start the lesson? Choose the option that best describes how comfortable you are with the skills on this slide. (1 point) A. I understand these skills and I can explain them to others. I am ready to start the lesson. B. I generally understand these skills. I am ready to start the lesson. C. I understand these skills when I have help. I should practice more before I start the lesson. D. I do not understand these skills. I need more practice before I start the lesson.

All of the answer choices are correct so it wouldn't matter which one you choice but choose whichever one is true for you. The teachers would want you to put A but don't put A if you cant do A. 1/1 point The final score is 1/1 (100%). The final adjusted score is 1/1 (100%). (That is if you put that answers.)

(3.4) Do you think you're ready to start the lesson?- Skills Check (1-1) 1. Do you think you are ready to start the lesson? Choose the option that best describes how comfortable you are with the skills on this slide. (1 point) A. I understand these skills and I can explain them to others. I am ready to start the lesson. B. I generally understand these skills. I am ready to start the lesson. C. I understand these skills when I have help. I should practice more before I start the lesson. D. I do not understand these skills. I need more practice before I start the lesson.

All of the answer choices are correct so it wouldn't matter which one you choice but choose whichever one is true for you. The teachers would want you to put A but don't put A if you cant do A. 1/1 point The final score is 1/1 (100%). The final adjusted score is 1/1 (100%). (That is if you put that answers.)

(3.5) Do you think you're ready to start the lesson?- Skills Check (1-1) 1. Do you think you are ready to start the lesson? Choose the option that best describes how comfortable you are with the skills on this slide. (1 point) A. I understand these skills and I can explain them to others. I am ready to start the lesson. B. I generally understand these skills. I am ready to start the lesson. C. I understand these skills when I have help. I should practice more before I start the lesson. D. I do not understand these skills. I need more practice before I start the lesson.

All of the answer choices are correct so it wouldn't matter which one you choice but choose whichever one is true for you. The teachers would want you to put A but don't put A if you cant do A. 1/1 point The final score is 1/1 (100%). The final adjusted score is 1/1 (100%). (That is if you put that answers.)

(3.6) Do you think you're ready to start the lesson?- Skills Check (1-1) 1. Do you think you are ready to start the lesson? Choose the option that best describes how comfortable you are with the skills on this slide. (1 point) A. I understand these skills and I can explain them to others. I am ready to start the lesson. B. I generally understand these skills. I am ready to start the lesson. C. I understand these skills when I have help. I should practice more before I start the lesson. D. I do not understand these skills. I need more practice before I start the lesson.

All of the answer choices are correct so it wouldn't matter which one you choice but choose whichever one is true for you. The teachers would want you to put A but don't put A if you cant do A. 1/1 point The final score is 1/1 (100%). The final adjusted score is 1/1 (100%). (That is if you put that answers.)

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 4. Find the least common multiple of x³-x²+ x-1 and x²-1. Write the answer in factored form. (1 point) A. (x+1)²(x-1) B. (x+1)(x-1)(x²+1) C. (x³-x²+x-1)(x²-1) D. (x+1)(x-1)(x²-1)

B. (x+1)(x-1)(x²+1) 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 10. The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 30 barrels of oil in traveling 85 miles at 42 mi/h. How many barrels of oil are used when the ship travels 26 miles at 54 mi/h? Round your answer to the nearest tenth of a barrel, if necessary. A. 2.3 barrels. B. 15.2 barrels C. 49.6 barrels. D. 9.2 barrels.

B. 15.2 barrels 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 6. The harmonic mean of two numbers, a and b, equals 2/ 1/a +1/b. As you vary the length of a violin or guitar string, its pitch changes. If a full-length string is 1 unit long, then many lengths that are simple fractions produce pitches that harmonize, or sound pleasing together. The harmonic mean relates two lengths that produce harmonious sounds. Find the harmonic mean for the string lengths of 1 and 1/2. (1 point) A. 3/2 B. 2/3 C. 2/5 D. 1

B. 2/3 1/1 point

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 2. What is the product in simplest form? State any restrictions on the variable. (1 point) 4a^5/7b^4 * 2b²/2a^4 A. 4a^9/7b^6, a=/0, b=/0 B. 4a/7b², a=/0, b=/0 C. 7b²/4a, a=/0, b=/0 D. 4/7a^9b^6, a=/0, b=/0

B. 4a/7b², a=/0, b=/0 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 1. Find the least common multiple of the following polynomials: 9(x+2)(2x-1) and 3(x+2). (1 point) A. (x+2)(2x-1) B. 9(x+2)(2x-1) C. (x+2) D. 9(x-2)(2x+1)

B. 9(x+2)(2x-1) 1/1 point

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 3. What is the quotient in simplest form? State any restrictions on the variable. (1 point) x²-16/x²+5x+6 ÷ x²+5x+4/x²-2x-8 A. (x-4)²/(x+3)(x+1); x ≠ -3, -1 B. (x-4)²(x+1)/(x+2)²(x+3); x ≠-3, -2, 4 C. (x-4)²/(x+3)(x+1); x ≠ -4, -3, -2, -1, 4 D. 1/(x+3)(x+1); x ≠ -4, -3, -2, -1, 4

C. (x-4)²/(x+3)(x+1); x ≠ -4, -3, -2, -1, 4 1/1 point

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 8. Simplify the complex fraction. (1 point) x+4x/y/7/3x A. 15x²/7y B. 7x(y+4)/3xy C. 3x²(y+4)/7y D. 3(y+4)/7y

C. 3x²(y+4)/7y 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 5. This graph of a function is a translation of y=4/x. what is an equation for the function? (Graphs are on google docs. Go to https://docs.google.com/document/d/19jW7945oXX8vLzAUEespVdVIIASra68BXCYZYxtwKqo/edit?usp=sharing to get the graphs) A. 4/x+2+6 B. 4/x+2-6 C. 4/x+6+2 D.4/x+6-2

C. 4/x+6+2 1/1 point

End of (3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 10. Find two rational expressions whose difference is equal to - x+4/4x. (1 point) A. x-1/4x - 4/x B. 2x/x-5 - 6/4x C. 4/x²-4x - x/4x-16 D. 1/x²-4 - x+1/2x-8

C. 4/x²-4x - x/4x-16 1/1 point The final score is 10/10 (100%). (That is if you put those answers.)

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 7. Simplify the complex fraction. (1 point) 4/x+3/1/x+3 A. 12x+4/x^2+3x B. 4x/3x+9 C. 4x/3x^2+10x+3 D. None of the above

C. 4x/3x^2+10x+3 1/1 point

End of (3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 12. You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function y= 100(0.05)+x(0.2)/100+x gives the concentration y of the blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye. How much of the 20% dye must you add to get a dye that is 12% concentrated? A. 62.5 mL B. 75 mL C. 87.5 mL D. 112.5 mL

C. 87.5 mL 1/1 point The final score is 12/12 (100%). (That is if you put those answers.)

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 3. Graph the function. (1 point) y=13/6x A. Graph is on google docs. B. Graph is on google docs. C. Graph is on google docs. D. Graph is on google docs. (Graphs are on google docs. Go to https://docs.google.com/document/d/19jW7945oXX8vLzAUEespVdVIIASra68BXCYZYxtwKqo/edit?usp=sharing to get the graphs)

C. The graph is on google docs. 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 7. Describe the vertical asymptote(s) and hole(s) for the graph of y=(x+2)(x+4)/(x+4)(x+1) A. asymptote: x=-1 and hole: x=4 B. asymptote: x=2 and hole: x=-1 C. asymptote: x=-1 and hole: x=-4 D.asymptote: x=1 and hole: x=4

C. asymptote: x=-1 and hole: x=-4 1/1 point

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 1. Simplify the rational expression. State any restrictions on the variable. (1 point) n^4-11n²+30/ n^4-7n²+10 A. n²-6/n²-2, n≠5, n≠2 B. -(n²-6)/n²-2, n≠±√5, n≠±√2 C. n²-6/n²-2, n≠±√5, n≠±√2 D. n²-6/n²-2, n≠5, n≠-2

C. n²-6/n²-2, n≠±√5, n≠±√2 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 6. Find any points of discontinuity for the rational function y=(x+6)(x+2)(x+8)/(x+9)(x+7) A. x=6, x=2, x=8 B. x=9, x=7 C. x=-9, x=-7 D. x=-6, x=-2, x=-8

C. x=-9, x=-7 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 9. Simplify the complex fraction 1/x/2/y. (1 point) A. 2/xy B. 2/x+y C. y/2x D. 1+y/2+x

C. y/2x 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 2. Suppose that y varies directly with x and inversely with z, and y=18 when x=15 and z=5. Write the equation that models the relationship. Then find y when x=21 and z=7. A. y= 5z/x; 5/3 B. y= 5x/z; 15 C. y=6x/z; 18 D. y=6z/x; 2

C. y=6x/z; 18

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 9. Solve the equation. Check the solution. (1 point) -2/x+4=4/x+3 A. -13/6 B. -11 C. -8/3 D. -11/3

D. -11/3 1/1 point

(3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 10. Solve the equation. Check the solution. (1 point) g+4/g-2=g-5/g-8 A. -22/3 B. 22 C. -22 D. 14

D. 14 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 5. For the image of the overhead projector to be in focus, the distance from the projector lens to the image, d_i, the projector lens focal length, f, and the distance from the transparency to the projector lens, d₀, must satisfy the thin lens equation 1/f=1/d_i+d₀. Which is the focal length of the projector lens if the transparency placed 4 inches from the projector lens is in focus on the screen, located 8 feet from the projector lens? (1 point) A. 0.375 in. B. 6 in. C. 0.167 in. D. 3.84 in.

D. 3.84 in. 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 2. Find the least common multiple of the following polynomials: 5y^2-80 and y+4. (1 point) A. (y+4)(y-4) B. (y+4) C. 5(y+10)(y-8) D. 5(y+4)(y-4)

D. 5(y+4)(y-4) 1/1 point

(3.5) Adding and Subtracting Rational Expressions Practice- Practice (1-10) 8. Find the difference. (1 point) 5x/x²-x-6 - 4/x²+4x+4 A. 5x-4/(x-3)(x+2)² B. 5x-4/(x-3) C. 5x²+6x+12/(x-3)(x+2) D. 5x²+6x+12/(x-3)(x+2)²

D. 5x²+6x+12/(x-3)(x+2)² 1/1 point

End of (3.6) Solving Rational Equations Quiz Part 1- Quiz (1-11) 11. Alicia can row 6 miles downstream in the same time it takes her to row 4 miles upstream. She rows downstream 3 miles/hour faster than she rows upstream. Find Alicia's rowing rate each way. Round your answers to the nearest tenth, if necessary. (1 point) A. 4 mi/h downstream, 2.7 mi/h upstream B. 20 mi/h downstream, 13.3 mi/h upstream C. 2.7 mi/h downstream, 4 mi/h upstream D. 9 mi/h downstream, 6 mi/h upstream

D. 9 mi/h downstream, 6 mi/h upstream 1/1 point The final score is 11/11 (100%). (That is if you put those answers.)

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 4. Sketch the asymptotes, and graph the function y= 5/(x-3)+2 A. The graph is on google docs. B. The graph is on google docs. C. The graph is on google docs. D. The graph is on google docs. (Graphs are on google docs. Go to https://docs.google.com/document/d/19jW7945oXX8vLzAUEespVdVIIASra68BXCYZYxtwKqo/edit?usp=sharing to get the graphs)

D. The graph is on google docs. 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 8. Find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10 A. y=0 B. y=6/5 C. y=3/8 D. There is no horizontal asymptote.

D. There is no horizontal asymptote. 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 11. The yearbook committee is distributing yearbooks to students by class. Each class has approximately the same number of students. The table shows the number of volunteers who helped to distribute the yearbooks to each of the four classes and the time needed to distribute the yearbooks. What function models the data? The number of volunteers (n): 2, 5, 8, 11 Time in minutes (t): 220, 88, 55, 40 A. nt= 80 B. nt= 180 C. nt= 222 D. nt= 440

D. nt= 440 1/1 point

(3.3) Rational Functions and Their Graphs Quiz Part 1- Quiz (1-12) 1. Suppose that w and t vary inversely and that t=1/5 when w=4. Write a function that models the inverse variation, and find t when w=9. (1 point) A. t= 1/5w; 4/45 B. t= 1/5w; 1/5 C. t= 1/20w; 1/80 D. t=4/5w; 4/45

D. t=4/5w; 4/45

(3.3) Rational Functions and Their Graphs Quiz Part 2- Quiz (1-3) 2. How do the graphs of y=1/x and y=5/x+6 compare? (2 points)

The answer is on a google doc. Go to https://docs.google.com/document/d/1sDyj-WrLJzRTEhbvE5RMxlu1AO50SaAM-xVXGJRUYOA/edit?usp=sharing to get the answer.

(3.3) Rational Functions and Their Graphs Quiz Part 2- Quiz (1-3) x: 3, 9, 13, 20 y: 9, 27, 39, 60 1. State whether the relationship between the variables in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write a function to model it. (2 points)

The answer is on a google doc. Go to https://docs.google.com/document/d/1sDyj-WrLJzRTEhbvE5RMxlu1AO50SaAM-xVXGJRUYOA/edit?usp=sharing to get the answer.

End of (3.3) Rational Functions and Their Graphs Quiz Part 2- Quiz (1-3) 3. Jane is organizing a fundraiser to buy a ping-pong table for the community center. The table costs $500.00. Jane is asking contributors to pay for an equal share of the cost of the table. She already has five contributors lined up. What function models the cost per share, C, with respect to the number of new contributors, n? How many new contributors must Jane recruit in order for the cost of each share to be $20.00? (2 points)

The answer is on a google doc. Go to https://docs.google.com/document/d/1sDyj-WrLJzRTEhbvE5RMxlu1AO50SaAM-xVXGJRUYOA/edit?usp=sharing to get the answer.

(3.8) Rational Functions Unit Test Part 1- Test (1-18) 1. (1 point)

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(3.6) Solving Rational Equations Quiz Part 2- Quiz (1-2) 1. The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator's needs? (3 points)

x will equal the speed of the boat in water. The speed of the boat traveling upstream is (u-6) mph, while the speed of the boat traveling downstream is (u+6) mph. The "time" equation is 22.5/u-6+22.5/u+6=9 Solve for u. For it, multiply both sides by 2*(u-6)*(u+6). You will get 45(u+6) + 45*(u-6) =18×(u²-36) 90u=18u²-648 18u²-90u-648=0 u²-5u-36=0 (u-9)*(u+4) = 0 The only positive root is u = 9. Answer: The speed of the boat in still water is 9 mph. Check: 22.5/9+6 + 22.5/9-6=9 hours Correct!! 3/3 points Feedback: OMIT