A2.2.19 Practice with Answer
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MATH 11
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Mathematics
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Dec 16, 2024
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Topic Rational FunctionsNAME DATE PERIOD PracticeEnd Behavior of Rational Functions1. The function f(x) =5x+2_x−3can be rewritten in the form f(x) =5 +17_x−3. What is the end behavior of y=f(x)?2. Rewrite the rational function g(x) =x2+7x−12_x+2in the form g(x) =p(x) +r_x+2, where p(x) is a polynomial and ris an integer.3. Match each polynomial with its end behavior as xgets larger and larger in the positive and negative directions.A. p(x) =3_x−11. The graph approaches y=2.B. q(x) =2x_x−12. The graph approaches y=3.C. r(x) =2x+3_x−13. The graph approaches y=2x+3.D. s(x) =2 x2+x+3_x−14. The graph approaches y=x2+x+1.E. t(x) =x3_x−15. The graph approaches y=0.4. Let the function Pbe defined by P(x) =x3+2 x2−13x+10. Mai divides P(x) by x+5 and gets:How could we tell by looking at the remainder that (x+5) is a factor? (Lesson 2-13)5. For the polynomial function f(x) =x4+3 x3−x2−3xwe have f(-3) =- 40, f(-2) =-6, f(-1) =0, f(0) =0, f(1) =30, f(2) =30, f(3) =144. Rewrite f(x) as a product of linear factors. (Lesson 2-15)x2-3x+2 x+5 x3+2x2-13x+10 _______- _____________x3-5x2-3 x2-13x________3x2+15x2x+10______-2x- 10 0Lesson 2-19 End Behavior of Rational Functions213Sample response: As xgets larger and larger in the positive or negative direction, the graph approaches y=5.g(x) =x+5 +- 22_x+2Sample response: Because the remainder is 0, (x+5) must be a factor.f(x) =x(x−1)(x+1)(x−3)
6. There are many cones with a volume of 60πcubic inches. The height h(r) in inches of one of these cones is a function of its radius rin inches where h(r) =180_r2. (Lesson 2-16)a. What is the height of one of these cones if its radius is 2 inches?b. What is the height of one of these cones if its radius is 3 inches?c. What is the height of one of these cones if its radius is 6 inches?7. A cylindrical can needs to have a volume of 10 cubic inches. There needs to be a label around the side of the can. The function S(r) =20_rgives the area of the label in square inches where ris the radius of the can in inches. (Lesson 2-17)a. As rgets closer and closer to 0, what does the behavior of the function tell you about the situation?b. As rgets larger and larger, what does the end behavior of the function tell you about the situation?8. Match each rational function with a description of its end behavior as xgets larger and larger. (Lesson 2-18)A. 9xB. 9_xC. 99x_xD. 99 +x_xE. 99x+9_xF. 99 +9x_x1. The value of the expression gets closer and closer to 0.2. The value of the expression gets closer and closer to 1.3. The value of the expression gets closer and closer to 9.4. The value of the expression gets closer and closer to 99.5. The value of the expression gets larger and 1. larger in the positive direction.6. The value of the expression gets larger and larger in the negative direction.214Unit 2 Polynomials and Rational FunctionsSample response: As the radius of the can gets closer and closer to 0, the area of the label gets larger and larger.45 inches20 inches5 inchesSample response: As the radius of the can gets larger and larger, the area of the label gets closer and closer to 0.