Chapter 2 Radicals and Rationals Practice Test

Transcription

1 Chapter Radicals and Rationals Practice Test Multiple Choice Identif the choice that best completes the statement or answers the question.. For the graph of shown below, which graph best represents? = f(x) x A. C. x x B. D. x x

2 . For the graph of shown below, which graph best represents? = f(x) x A. C. x x B. D. x x

3 . For the graph of shown below, what are the domain and range of? x = f(x) A. domain: ; range: B. domain: ; range: C. domain: ; range: D. domain: ; range:. Use graphing technolog to solve: Give the solution to the nearest tenth. A. C. B. D.. The graph of which function below has a hole? A. C. B. D.. What is the equation of the vertical asmptote of the graph of this function? A. C. B. D. The graph has no vertical asmptote. 7. The graph of which function below has vertical asmptote and no horizontal asmptote? A. C. B. D.

4 . State the domain of this rational function. x A. domain: C. domain: B. domain: D. domain: 9. For the graph of this rational function, state the domain and write the equations of an asmptotes and the coordinates of an hole. x A. domain: and ; vertical asmptotes:, ; horizontal asmptote: B. domain: and ; vertical asmptotes:, ; horizontal asmptote: C. domain: ; hole: vertical asmptote: ; horizontal asmptote: D. domain: and ; hole: vertical asmptote: ; horizontal asmptote:

5 0. For the graph of this rational function, state the domain and write the equations of an asmptotes. x A. domain: ; vertical asmptote: ; oblique asmptote: B. domain: ; vertical asmptote: ; oblique asmptote: C. domain: ; vertical asmptote: ; oblique asmptote: D. domain: ; vertical asmptote: ; oblique asmptote:. For the graph of this rational function, identif the equations of an asmptotes and the coordinates of an hole. A. The graph has a vertical asmptote at, and a horizontal asmptote at. B. The graph has vertical asmptotes at and, and a horizontal asmptote at. C. The graph has a vertical asmptote at, a hole at (, ), and a horizontal asmptote at. D. The graph has a vertical asmptote at, a hole at (, ), and a horizontal asmptote at.. For the graph of this rational function, identif the equations of an asmptotes and the coordinates of an hole. A. The graph has holes at and. B. The graph has a vertical asmptote at, and an oblique asmptote at. C. The graph has vertical asmptotes at, and a horizontal asmptote at. D. The graph has vertical asmptotes at, and a horizontal asmptote at.

6 . What is the solution of this radical equation, to the nearest tenth if necessar? A. C. B. or D. or. What is the solution of this radical equation, to the nearest tenth if necessar? A. or C. B. or D.. Which graph below represents this function? A. C. x x B. D. x x

7 . Which function below describes this graph? 0 0 x A. C. B. D. 7. Which function below describes this graph? x A. C. B. D.

8 . Which graph represents the function? A. C. x x B. D. x x

9 9. Which graph represents the function? A. C. x x B. D. x x Short Answer. For the graph of shown below, sketch the graph of x = f(x)

10 . Use technolog to graph this function, then complete the table below. Vertical Asmptote(s) Horizontal Asmptote Non-permissible values of x. Does the graph of this function have an holes or vertical asmptotes? Write the coordinates of an holes and the equations of an vertical asmptotes.. Does the graph of this function have a horizontal asmptote? If it does, write its equation.. Sketch the graph of this function. x

11 . Sketch the graph of this function. x 7. Sketch the graph of this function. x Problem. The time, t seconds, for one oscillation of a pendulum can be calculated b using the formula, where l is the length of the pendulum in metres. One oscillation of a pendulum takes s. What is the length of the pendulum? Give our answer to the nearest tenth of a metre.

12 . For the graph of this rational function: a) Determine an non-permissible values of x, and whether each indicates a hole or a vertical asmptote. b) Write the coordinates of an hole. Write the equation of an vertical asmptote. Show our work.. Two cars travel to Edmonton at the same time. Car A travels 00 km in the same time it takes Car B to travel 70 km. Car A travels an average of km/h faster than Car B. A rational equation that relates the average speeds of the two cars is: the average speed of each car, to the nearest kilometre per hour., where v kilometres per hour is the average speed of Car B. Determine. Create an equation for a rational function whose graph is the line with a single hole. Explain our thinking.. Sketch the graph of this function, and state the domain and range. Show our work. x

13 Chapter Radicals and Rationals Practice Test Answer Section MULTIPLE CHOICE. ANS: A PTS: DIF: Eas REF:. Properties of Radical Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding. ANS: A PTS: DIF: Moderate REF:. Properties of Radical Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding. ANS: D PTS: DIF: Moderate REF:. Properties of Radical Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge Conceptual Understanding. ANS: D PTS: DIF: Moderate REF:. Properties of Radical Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge. ANS: C PTS: DIF: Eas REF:. Math Lab: Graphing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding. ANS: B PTS: DIF: Eas REF:. Math Lab: Graphing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge 7. ANS: B PTS: DIF: Moderate REF:. Math Lab: Graphing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding. ANS: C PTS: DIF: Eas REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge 9. ANS: B PTS: DIF: Eas REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge 0. ANS: B PTS: DIF: Eas REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge. ANS: C PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge. ANS: D PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge. ANS: B PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge. ANS: A PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge. ANS: C PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge Conceptual Understanding. ANS: C PTS: DIF: Moderate REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding 7. ANS: A PTS: DIF: Moderate

14 REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding. ANS: B PTS: DIF: Moderate REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Radical and Rational Functions KEY: Conceptual Understanding 9. ANS: A PTS: DIF: Moderate REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding SHORT ANSWER. ANS: = f(x) x = f(x) PTS: DIF: Moderate REF:. Properties of Radical Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge. ANS: Vertical Asmptote(s) Horizontal Asmptote Non-permissible values of x none none PTS: DIF: Eas REF:. Math Lab: Graphing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge. ANS: The graph does not have an holes or vertical asmptotes. PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge. ANS: The graph has a horizontal asmptote with equation:. PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions

15 KEY: Conceptual Understanding Procedural Knowledge. ANS: x PTS: DIF: Eas REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge Communication. ANS: x PTS: DIF: Moderate REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge Communication 7. ANS:

16 x PTS: DIF: Moderate REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge Communication PROBLEM. ANS: From the problem, Substitute the value of t into the equation. Move all the terms to one side. Write a related function. Use technolog to graph the function. Determine the approximate zero:. So, the pendulum is approximatel. m long. PTS: DIF: Moderate REF:. Properties of Radical Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge Problem-Solving Skills. ANS: a) Factor the denominator to determine the non-permissible values of x.

17 So, the non-permissible values are and. Neither factor of the denominator is a factor of the numerator, so both non-permissible values indicate vertical asmptotes. b) The vertical asmptotes have equations and. PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge Communication. ANS: Write a related function: Use graphing technolog to determine the zero: So Car B is travelling at an average speed of km/h, while Car A is travelling km/h faster, at an average speed of 00 km/h. PTS: DIF: Moderate REF:. Analzing Rational Functions LOC:.RF TOP: Relations and Functions KEY: Procedural Knowledge Problem-Solving Skills. ANS: The equation of the rational function will simplif to, and the numerator and denominator of the function will have a common factor of the form for some real number a. Students answers will var.for example: The graph of, or is the line with a hole at. x PTS: DIF: Difficult REF:. Analzing Rational Functions

18 LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Communication Problem-Solving Skills. ANS: The denominator is, so the graph has a non-permissible value of x at. Factor: Simplif:, So, the graph of the rational function is the line, with a hole at. The -coordinate of the hole is:, or. So, the hole has coordinates (, ). Draw the line with an open circle at (, ). The function has domain range. and x PTS: DIF: Moderate REF:. Sketching Graphs of Rational Functions LOC:.RF TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge Communication