9 RATIONAL FUNCTIONS TEST REVIEW 2017 - Loudoun County Public Schools
RATIONAL FUNCTIONS TEST REVIEW Name: SECTION 1: OPERATIONS OF RATIONAL EXPRESSIONS Complete the operation or simplify. 1. 4x 12 2 x 2x 15 2. 15x3 y5 6xy3 2xy 9x 4 y 3. 8x 3 125 x 5 2 2x 5 x 25 4. x 2 6x x 2 2x 8 2 x 8x 12 x 3 8
5. x 2 9x 22 x 2 5x 24 x 2 x 3 7. 5x x 3 x 2 x 2 6. 4x 4x 1 x 3 x 3 8. 5x 2 3y 15
9. 2x 5 2 x 3 x 3x Factor each expression completely. 11. 64x2 – 121 13. 6x2 – 7x – 5 x 10. x2 x 12. x3 – 125 14. x2 – 15x 50 12 5 12x 48
15. 3x3 – 24 16. x2 – 13x – 30 17. 27x3 64 18. x2 – 1 19. x2 – 64x 20. 20x2 26x – 6 21. 24x4 – 8x3 4x 22. 4x2 49 23. 3x2 24x 48 24. 25x2 – 60x 36
SECTION 2: GRAPHING RATIONAL FUNCTIONS 1. How do you find a vertical asymptote of a rational function? 2. How do you find a horizontal asymptote when graphing if the degree is larger on the denominator? 3. How do you find a horizontal asymptote when graphing if the degree of the numerator is the same as the degree of the denominator? 4. How do you find a removable discontinuity of a rational function? 5. How do you find the domain and range of a rational function? 6. How do you find the degree of a polynomial in standard form? 7. How do you find the degree of a polynomial in factored form? Circle the asymptotes of the following function. 8. y x 1 9. y x 5 Circle all that apply. 3 4 x 1 x –1 x 4 y 3 y 1 y 4 x –5 y 0 y 1 y 5 10 x 2 25 x 0
10. Identify the vertical asymptote, horizontal asymptote, domain and range of each equation. Vertical Asymptote Horizontal Asymptote Domain Range a. b. c. d. Identify the vertical asymptote, horizontal asymptote, domain and range of the graph. 11. 12. Vertical Asymptote: Vertical Asymptote: Horiztonal Asymptote: Horiztonal Asymptote: Domain: Domain: Range: Range:
13. y 6 1 x 2 VA: Domain: HA: Range: 14. Table Graph Table Graph f (x) 2x x 5 VA: Domain: HA: Range:
15. f (x) 3x 2 3 x2 9 VA: Domain: HA: Range: 16. x2 9 f (x) 2 x 8x 15 VA: Domain: HA: Range: Table Graph Table Graph
VARIATION VARIATION: 1. Direct variation formula: 2. Inverse variation formula: 3. Joint variation formula: Determine if the equation or situation represents direct, inverse, or joint variation, or neither. 4. d kst 5. m k r 6. s kpr 7. a 5 b 8. y x 10 9. y s 7 Translate each situation into an equation. Do Not Solve! 10. An equation shows m is directly proportional to n and inversely proportional to s cubed. When m 5, then n 160 and s 2. What is the constant of proportionality? Write your answer as a fraction. 11. The weight, w, that a column of a bridge can support varies directly as the fourth power of its diameter, d, and inversely as the square of its length, l. 12. The number, n, of grapefruit that can fit into a box is inversely proportional to the cube of the diameter, d, of each grapefruit.
13. An equation shows m is directly proportional to n and inversely proportional to s cubed. When m –4, then n 160 and s 2. What is the constant of proportionality? 14. The variable z varies jointly with x and y. Write an equation relating x, y, and z when x -4, y 3, and z 2. 15. The amount of money earned at your job ( m ) varies directly with the number of hours (h) you work. The first day of work you earned 57 after working 6 hours. You are trying to save money to go to buy a new car to take to college next year. How many hours will you need to work in order to save 4750? 16. The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the speed and inversely as the radius of the curve. Suppose a 3,960 lb. force is required to keep a 2,200 lb. car traveling at 30 mph from skidding on a curve of radius 500 ft. How much force is required to keep a 3,000 lb. car traveling at 45 mph from skidding on a curve of radius 400 ft.?
2xy 6xy3 9x4y 3. 8x3 . How do you find the domain and range of a rational function? 6. How do you find the degree of a polynomial in standard form? 7. How do you find the degree of a polynomial in factored form? Circle the asymptotes of the following function. Circle all that apply. 8. y 3 x 1 4
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Ch 2. Functions and Graphs 2.4 Polynomial and Rational Functions Rational Functions Just as rational numbers are de ned in terms of quotients of integers, rational functions are de ned in terms of quotients of polynomials. De nition (Rational Function) A rational function is any function that can be written in the form f(x) n(x) d(x); d(x) 6 0
Rational Rational Rational Irrational Irrational Rational 13. 2 13 14. 0.42̅̅̅̅ 15. 0.39 16. 100 17. 16 18. 43 Rational Rational Rational Rational Rational Irrational 19. If the number 0.77 is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational?
Unit 5: Graphing Rational Functions In the previous unit, we studied the long-run behavior of rational functions. Now we will study the short-run behavior so that we can sketch the complete graphs of rational functions. Like polynomial functions, the short-run behavior of rational functions includes roots and y-intercepts.
Translate simple rational functions. Graph other rational functions. Graphing Simple Rational Functions A rational function has the form f(x) p(x) —, where q(x) p(x) and q(x) are polynomials and q(x) 0. The inverse variation function f(x) a — is a rational function. The graph x of this function when a 1 is shown below. Graphing a .
Translate simple rational functions. Graph other rational functions. Graphing Simple Rational Functions A rational function has the form f(x) p(x) —, where q(x) p(x) and q(x) are polynomials and q(x) 0. The inverse variation function f(x) a — is a rational function. The graph x of this function when a 1 is shown below. Graphing a .
A) Graphing Simple Rational Functions B) Graphing More Complicated Rational Functions 4) Rational Expressions and Equations A) Adding and Subtracting Rational Expressions B) Multiplying and Dividing Rational Expressions C) Solving Rational Equations 4th 9 Weeks: 1) Radical Functions A) Inverses of Simple Quadratic and Cubic Functions
1. Rational Numbers: Students will understand that a rational number is an integer divided by an integer. Students will convert rational numbers to decimals, write decimals as fractions and order rational numbers. 2. Adding Rational Numbers: Students will add rational numbers. 3. Subtracting Rational Numbers: Students will subtract rational .
