1. An equation with at least one ratio of two polynomials is called: a. quadratic equation b. linear equation c. rational equation d. radical equation 2. The f(x) = x^2 + 2x + 8 is... 1. An equation with at least one ratio of two polynomials is called: a. quadratic equation b. linear equation c. rational equation d. radical equation 2. The f(x) = x^2 + 2x + 8 is an example of: a. Rational expression b. Rational Equation c. Rational function d. Rational inequality 3. Which of the following is a rational expression? a. f(x) = (x + 1)/(x - 3) b. (3/x - 4)/(x + 8) c. (3)/(x) d. (x^2 - 2x + 1)/(x - 3) 4. Which of the following expressions that can be written as the ratio of two polynomial functions: a. rational function b. rational equation c. rational inequality d. irrational expression 5. How do you determine the y-intercept of a rational function? a. By letting x = 0. b. By solving the equation f(x) = 0. c. By solving the x-intercepts of the graph of the function. d. By factoring the numerator and denominator and setting each factor equal to zero. 6. How will you describe the horizontal asymptote of a rational function of n > m? a. no horizontal asymptote b. y = 0 c. y = a/b d. a and 7. All of the following are rational inequalities except a. 1/x < 0 b. √(3x)/(x + 5) > 0 c. (x - 4)/(x - 8) < 0 d. -1/(x^2 - 2x + 1) ≤ 0 8. Which of the following is the extraneous solution of x/(x + 1) = 8? a. x = 2 b. x = -2 c. x = 5 d. d = -5 9. Which factor(s) of a rational function’s numerator and denominator are important when determining its horizontal asymptote? a. constant terms b. leading terms c. linear terms d. quadratic terms 10. Which of the following does NOT represent a symbol for rational inequality? a. ≤ b. = c. ≠ d. > 11. Which interval notation represents the set of numbers that are greater than or equal to -1, but are less than 9? a. (-1, 9) b. [-1, 9] c. (-1, 9) d. [-1, 9] 12. Find the domain of the function f(x) = 5/(x - 3): a. {x|x ∈ ℝ except 3} b. {x|x ∈ ℝ except -3} c. {x|x ∈ ℝ except -3/2} d. {x|x ∈ ℝ except 5/2} 13. What is the value of x in the equation 4/(2x) - 1/5? a. x = 5/2 b. x = 10 c. x = 5/2 d. x = 5 14. Jepoi can iron clothes in 3 hours. If he and his brother Jeffzky work together, they can finish the job in 2 hours. What part of the job can Jepoi do in an hour? a. 1/3 b. 1/2 c. 1/6 d. 1/x 15. Find the solution set of the inequality (5/7) - (x/4) < 9/10: a. (-18, ∞) b. (-∞, 18) c. [-18, ∞) d. [18, ∞) 16. Which of the following is an example of Rational Function? a. x + 2y = 0 b. 2x - 1 c. x^2 > 1 d. f(x) = x/2
Understand the Problem
The question presents multiple-choice queries related to rational functions, inequalities, and algebraic expressions. It requires identifying correct definitions, properties, and solving equations or inequalities involving rational functions.
Answer
1. c 2. c 3. a 4. a 5. a 6. a 7. b 8. b 9. b 10. b 11. b 12. a 13. a 14. a 15. a 16. d
["1. c. rational equation","2. c. Rational function","3. a. f(x) = (x + 1)/(x - 3)","4. a. rational function","5. a. By letting x = 0.","6. a. no horizontal asymptote","7. b. \u221a(3x)/(x + 5) > 0","8. b. x = -2","9. b. leading terms","10. b. =","11. b. [-1, 9]","12. a. {x|x \u2208 \u211d except 3}","13. a. x = 5/2","14. a. 1/3","15. a. (-18, \u221e)","16. d. f(x) = x/2"]
Answer for screen readers
["1. c. rational equation","2. c. Rational function","3. a. f(x) = (x + 1)/(x - 3)","4. a. rational function","5. a. By letting x = 0.","6. a. no horizontal asymptote","7. b. \u221a(3x)/(x + 5) > 0","8. b. x = -2","9. b. leading terms","10. b. =","11. b. [-1, 9]","12. a. {x|x \u2208 \u211d except 3}","13. a. x = 5/2","14. a. 1/3","15. a. (-18, \u221e)","16. d. f(x) = x/2"]
More Information
These questions test understanding of rational expressions, functions, and equations, including their properties and solutions.
Tips
Common mistakes include misidentifying types of equations or functions and incorrectly solving algebraic expressions.
AI-generated content may contain errors. Please verify critical information