MHF4U1- ASSIGNMENT CHAPTER 3 A



MHF4U1- ASSIGNMENT CHAPTER 3 A NAME:__________________________

True/False

Indicate whether the statement is true or false.

____ 1. The reciprocal of every linear function has a vertical asymptote.

____ 2. If the slope of a function is positive then the function itself is increasing.

____ 3. All rational functions have at least one vertical asymptote.

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 4. Which of the following is the reciprocal of a linear function?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 5. Which of the following is the reciprocal of a quadratic function?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |none of the above |

____ 6. Which of the following has a horizontal asymptote at [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |all of the above |

____ 7. What is true about the function [pic] as [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |f(x) is undefined |

____ 8. What is the x-intercept of [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |There is no x-intercept. |

____ 9. What is the y-intercept of the function [pic]?

|a. |2 |c. |1 |

|b. |–3 |d. |0 |

____ 10. What is the equation of the horizontal asymptote of [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 11. What is the value of k in the function[pic] if its graph passes through the point (5, –0.35) ?

|a. |10 |c. |[pic] |

|b. |[pic] |d. |No such k exists |

____ 12. Which function is always positive?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |B and C |

____ 13. Which function has a y-intercept of [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |all of the above |

____ 14. What is true about the function [pic], as [pic]?

|a. |[pic] from below |c. |[pic] |

|b. |[pic] from above |d. |[pic] |

____ 15. Over what interval(s) is the graph of the rational function decreasing?

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 16. Which function has a y-intercept of [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 17. Over what interval is the graph of the rational function positive but decreasing?

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 18. Which function has a vertical asymptote at [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 19. What is the equation for the horizontal asymptote of the graph of the function shown?

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 20. For what interval(s) is the graph of the rational function negative?

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 21. Where is the function [pic] increasing?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 22. What is true about the function [pic] as [pic]?

|a. |[pic] from above |c. |[pic] from above |

|b. |[pic] from below |d. |[pic] from below |

____ 23. What is the value of k in the function [pic] if its graph passes through the point (2, 4.2)?

|a. |21.2 |c. |17 |

|b. |6 |d. |none of the above |

Completion

Complete each statement.

24. The rational function [pic] has a vertical asymptote with equation _______________.

25. Any rational function of the form [pic] always has a y-intercept of _______________.

Matching

Match each graph of a rational function with its equation.

|a. |[pic] |e. |[pic] |

|b. |[pic] |f. |[pic] |

|c. |[pic] |g. |[pic] |

|d. |[pic] |h. |[pic] |

____ 26.

[pic]

____ 27.

[pic]

____ 28.

[pic]

____ 29.

[pic]

____ 30.

[pic]

Short Answer

31. Determine the interval(s) where the function [pic] is

a) positive

b) increasing

32. Determine an equation in the form [pic] for a function with a vertical asymptote at [pic] and a y-intercept of [pic].

33. Determine the approximate slope of the tangent to the curve[pic] at [pic], to one decimal place.

34. Consider the function [pic].

a) Determine the key features of the function:

i) domain and range

ii) intercepts

iii) equations of any asymptotes

iv) intervals where the function is increasing and intervals where the function is decreasing

b) Sketch a graph of the function.

35. Consider the function [pic].

a) Determine the key features of the function:

i) domain and range

ii) intercepts

iii) equations of any asymptotes

iv) intervals where the function is increasing and intervals where the function is decreasing

b) Sketch a graph of the function.

Problem

36. The time, in hours, that it takes Alistair to jog 5 km is inversely proportional to his average speed, in kilometres per hour.

a) Write a function to represent the time as a function of the speed.

b) Sketch a graph of this function.

c) If Alistair jogs at 4.5 km/h, how long does it take him to complete a 5 km run, to the nearest minute?

d) Describe the rate of change in Alistair’s run times as his average speed increases.

MHF4U1- ASSIGNMENT CHAPTER 3 A

Answer Section

TRUE/FALSE

1. ANS: T PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function, vertical asymptote

2. ANS: T PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Sections 3.2, 3.3 LOC: C2.1, C2.2 TOP: Polynomial and Rational Functions

KEY: rational function, increasing

3. ANS: F PTS: 1 DIF: 1

REF: Knowledge and Understanding; Thinking OBJ: Section 3.2

LOC: C2.1 TOP: Polynomial and Rational Functions KEY: vertical asymptote

MULTIPLE CHOICE

4. ANS: D PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: reciprocal of linear function

5. ANS: B PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.2 LOC: C2.1, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: reciprocal of quadratic function

6. ANS: D PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: reciprocal of linear function, horizontal asymptote

7. ANS: B PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function

8. ANS: D PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function

9. ANS: A PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function, y-intercept

10. ANS: A PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function, horizontal asymptote

11. ANS: A PTS: 1 DIF: 2

REF: Knowledge and Understanding; Application OBJ: Section 3.1

LOC: C3.6, C3.7 TOP: Polynomial and Rational Functions KEY: reciprocal of linear function

12. ANS: D PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Sections 3.1, 3.2 LOC: C2.1, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: reciprocal of quadratic function, positive

13. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.2 LOC: C2.1, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: reciprocal of quadratic function, y-intercept

14. ANS: C PTS: 1 DIF: 2

REF: Knowledge and Understanding; Thinking OBJ: Section 3.2

LOC: C2.1 TOP: Polynomial and Rational Functions KEY: reciprocal of quadratic function

15. ANS: C PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Section 3.2 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of quadratic function, decreasing

16. ANS: D PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.3 LOC: C2.2, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: linear expressions in numerator and denominator, y-intercept

17. ANS: B PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Section 3.2 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of quadratic function, positive, decreasing

18. ANS: B PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.3 LOC: C2.2, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: linear expressions in numerator and denominator, vertical asymptote

19. ANS: D PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.3 LOC: C2.2 TOP: Polynomial and Rational Functions

KEY: linear expressions in numerator and denominator, horizontal asymptote

20. ANS: C PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.3 LOC: C2.2 TOP: Polynomial and Rational Functions

KEY: linear expressions in numerator and denominator, negative

21. ANS: D PTS: 1 DIF: 2

REF: Knowledge and Understanding; Thinking OBJ: Section 3.3

LOC: C2.2 TOP: Polynomial and Rational Functions

KEY: linear expressions in numerator and denominator, increasing

22. ANS: D PTS: 1 DIF: 2

REF: Knowledge and Understanding; Thinking OBJ: Section 3.3

LOC: C2.2 TOP: Polynomial and Rational Functions

KEY: linear expressions in numerator and denominator

23. ANS: C PTS: 1 DIF: 2

REF: Knowledge and Understanding; Thinking; Application OBJ: Section 3.3

LOC: C3.6, C3.7 TOP: Polynomial and Rational Functions

KEY: linear expressions in numerator and denominator

COMPLETION

24. ANS: [pic]

PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function, vertical asymptote

25. ANS: [pic]

PTS: 1 DIF: 1 REF: Knowledge and Understanding

OBJ: Section 3.2 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of quadratic function, y-intercept

MATCHING

26. ANS: C PTS: 1 DIF: 2

REF: Knowledge and Understanding; Application OBJ: Sections 3.1, 3.2, 3.3

LOC: C2.1, C2.2, C2.3, D3.1

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: rational functions, graphs

27. ANS: H PTS: 1

28. ANS: F PTS: 1

29. ANS: E PTS: 1

30. ANS: A PTS: 1

SHORT ANSWER

31. ANS:

a) x < –5

b) [pic]

PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function, positive, increasing

32. ANS:

[pic]

PTS: 1 DIF: 2 REF: Knowledge and Understanding; Thinking; Application

OBJ: Section 3.1 LOC: C2.1, C3.7 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function

33. ANS:

[pic]

PTS: 1 DIF: 2 REF: Knowledge and Understanding; Application

OBJ: Section 3.3 LOC: C2.2, D1.7, D1.8

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: instantaneous rate of change NOT: Students may use technology to confirm answer

34. ANS:

a) i) [pic]

ii) x-intercept: none, y-intercept: [pic]

iii) [pic]

iv) increasing for no values of x, decreasing for [pic]

b)

[pic]

PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Section 3.1 LOC: C2.1, C2.3 TOP: Polynomial and Rational Functions

KEY: reciprocal of linear function, key features, graph

35. ANS:

a) i) [pic]

ii) x-intercept: [pic], y-intercept: [pic]

iii) [pic]

iv) increasing for no values of x, decreasing for [pic]

b)

[pic]

PTS: 1 DIF: 2 REF: Knowledge and Understanding

OBJ: Section 3.3 LOC: C2.2, C2.3 TOP: Polynomial and Rational Functions

KEY: linear expressions in numerator and denominator, key features, graph

PROBLEM

36. ANS:

a) [pic]

b)

[pic]

c) 1 h and 7 min

d) As his speed increases, the rate of change of his run time decreases.

PTS: 1 DIF: 2

REF: Knowledge and Understanding; Application; Communication

OBJ: Section 3.1 LOC: C2.1, C2.3, C3.7, D1.3, D1.7, D1.9, D2.2

TOP: Polynomial and Rational Functions, Characteristics of Functions

KEY: word problem, reciprocal of linear function, rate of change, graph

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