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.
c.
b.
____
d.
5. Which of the following is the reciprocal of a quadratic function?
a.
c.
b.
____
d. none of the above
6. Which of the following has a horizontal asymptote at
a.
c.
b.
____
d. all of the above
7. What is true about the function
as
a.
b.
____
____
8. What is the x-intercept of
?
?
c.
d. f(x) is undefined
?
a.
c.
b.
d. There is no x-intercept.
9. What is the y-intercept of the function
a. 2
b. –3
?
c. 1
d. 0
____ 10. What is the equation of the horizontal asymptote of
a.
b.
?
c.
d.
if its graph passes through the point (5, –0.35) ?
____ 11. What is the value of k in the function
a. 10
c.
b.
d. No such k exists
____ 12. Which function is always positive?
a.
b.
c.
d. B and C
____ 13. Which function has a y-intercept of ?
a.
c.
b.
d. all of the above
____ 14. What is true about the function
a.
b.
from below
from above
, as
?
c.
d.
____ 15. Over what interval(s) is the graph of the rational function decreasing?
a.
b.
____ 16. Which function has a y-intercept of ?
c.
d.
a.
c.
b.
d.
____ 17. Over what interval is the graph of the rational function positive but decreasing?
a.
b.
____ 18. Which function has a vertical asymptote at
a.
b.
c.
d.
?
c.
d.
____ 19. What is the equation for the horizontal asymptote of the graph of the function shown?
a.
b.
c.
d.
____ 20. For what interval(s) is the graph of the rational function negative?
a.
b.
c.
d.
____ 21. Where is the function
increasing?
a.
b.
c.
d.
____ 22. What is true about the function
a.
b.
as
from above
from below
____ 23. What is the value of k in the function
a. 21.2
b. 6
?
c.
from above
d.
from below
if its graph passes through the point (2, 4.2)?
c. 17
d. none of the above
Completion
Complete each statement.
24. The rational function
25. Any rational function of the form
has a vertical asymptote with equation _______________.
always has a y-intercept of _______________.
Matching
Match each graph of a rational function with its equation.
a.
e.
____ 26.
____ 27.
____ 28.
____ 29.
b.
f.
c.
g.
d.
h.
____ 30.
Short Answer
31. Determine the interval(s) where the function
is
a) positive
b) increasing
32. Determine an equation in the form
intercept of
for a function with a vertical asymptote at
and a y-
.
33. Determine the approximate slope of the tangent to the curve
34. Consider the function
at
, to one decimal place.
.
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
.
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:
OBJ:
KEY:
2. ANS:
OBJ:
KEY:
3. ANS:
REF:
LOC:
T
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of linear function, vertical asymptote
T
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Sections 3.2, 3.3
LOC: C2.1, C2.2
TOP: Polynomial and Rational Functions
rational function, increasing
F
PTS: 1
DIF: 1
Knowledge and Understanding; Thinking
OBJ: Section 3.2
C2.1
TOP: Polynomial and Rational Functions KEY: vertical asymptote
MULTIPLE CHOICE
4. ANS:
OBJ:
TOP:
KEY:
5. ANS:
OBJ:
TOP:
KEY:
6. ANS:
OBJ:
TOP:
KEY:
7. ANS:
OBJ:
KEY:
8. ANS:
OBJ:
KEY:
9. ANS:
OBJ:
KEY:
10. ANS:
OBJ:
KEY:
11. ANS:
REF:
LOC:
12. ANS:
OBJ:
TOP:
D
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1, D3.1
Polynomial and Rational Functions, Characteristics of Functions
reciprocal of linear function
B
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.2
LOC: C2.1, D3.1
Polynomial and Rational Functions, Characteristics of Functions
reciprocal of quadratic function
D
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1, D3.1
Polynomial and Rational Functions, Characteristics of Functions
reciprocal of linear function, horizontal asymptote
B
PTS: 1
DIF: 2
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of linear function
D
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of linear function
A
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of linear function, y-intercept
A
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.1
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of linear function, horizontal asymptote
A
PTS: 1
DIF: 2
Knowledge and Understanding; Application
OBJ: Section 3.1
C3.6, C3.7
TOP: Polynomial and Rational Functions KEY: reciprocal of linear function
D
PTS: 1
DIF: 2
REF: Knowledge and Understanding
Sections 3.1, 3.2
LOC: C2.1, D3.1
Polynomial and Rational Functions, Characteristics of Functions
KEY:
13. ANS:
OBJ:
TOP:
KEY:
14. ANS:
REF:
LOC:
15. ANS:
OBJ:
KEY:
16. ANS:
OBJ:
TOP:
KEY:
17. ANS:
OBJ:
KEY:
18. ANS:
OBJ:
TOP:
KEY:
19. ANS:
OBJ:
KEY:
20. ANS:
OBJ:
KEY:
21. ANS:
REF:
LOC:
KEY:
22. ANS:
REF:
LOC:
KEY:
23. ANS:
REF:
LOC:
KEY:
reciprocal of quadratic function, positive
C
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.2
LOC: C2.1, D3.1
Polynomial and Rational Functions, Characteristics of Functions
reciprocal of quadratic function, y-intercept
C
PTS: 1
DIF: 2
Knowledge and Understanding; Thinking
OBJ: Section 3.2
C2.1
TOP: Polynomial and Rational Functions KEY: reciprocal of quadratic function
C
PTS: 1
DIF: 2
REF: Knowledge and Understanding
Section 3.2
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of quadratic function, decreasing
D
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.3
LOC: C2.2, D3.1
Polynomial and Rational Functions, Characteristics of Functions
linear expressions in numerator and denominator, y-intercept
B
PTS: 1
DIF: 2
REF: Knowledge and Understanding
Section 3.2
LOC: C2.1
TOP: Polynomial and Rational Functions
reciprocal of quadratic function, positive, decreasing
B
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.3
LOC: C2.2, D3.1
Polynomial and Rational Functions, Characteristics of Functions
linear expressions in numerator and denominator, vertical asymptote
D
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.3
LOC: C2.2
TOP: Polynomial and Rational Functions
linear expressions in numerator and denominator, horizontal asymptote
C
PTS: 1
DIF: 1
REF: Knowledge and Understanding
Section 3.3
LOC: C2.2
TOP: Polynomial and Rational Functions
linear expressions in numerator and denominator, negative
D
PTS: 1
DIF: 2
Knowledge and Understanding; Thinking
OBJ: Section 3.3
C2.2
TOP: Polynomial and Rational Functions
linear expressions in numerator and denominator, increasing
D
PTS: 1
DIF: 2
Knowledge and Understanding; Thinking
OBJ: Section 3.3
C2.2
TOP: Polynomial and Rational Functions
linear expressions in numerator and denominator
C
PTS: 1
DIF: 2
Knowledge and Understanding; Thinking; Application
OBJ: Section 3.3
C3.6, C3.7
TOP: Polynomial and Rational Functions
linear expressions in numerator and denominator
COMPLETION
24. ANS:
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:
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:
REF:
LOC:
TOP:
KEY:
27. ANS:
28. ANS:
29. ANS:
30. ANS:
C
PTS: 1
DIF: 2
Knowledge and Understanding; Application
OBJ:
C2.1, C2.2, C2.3, D3.1
Polynomial and Rational Functions, Characteristics of Functions
rational functions, graphs
H
PTS: 1
F
PTS: 1
E
PTS: 1
A
PTS: 1
Sections 3.1, 3.2, 3.3
SHORT ANSWER
31. ANS:
a) x < –5
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, positive, increasing
32. ANS:
PTS: 1
DIF: 2
OBJ: Section 3.1
LOC: C2.1, C3.7
KEY: reciprocal of linear function
33. ANS:
PTS:
OBJ:
TOP:
KEY:
34. ANS:
REF: Knowledge and Understanding; Thinking; Application
TOP: Polynomial and Rational Functions
1
DIF: 2
REF: Knowledge and Understanding; Application
Section 3.3
LOC: C2.2, D1.7, D1.8
Polynomial and Rational Functions, Characteristics of Functions
instantaneous rate of change
NOT: Students may use technology to confirm answer
a) i)
ii) x-intercept: none, y-intercept:
iii)
iv) increasing for no values of x, decreasing for
b)
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)
ii) x-intercept:
, y-intercept:
iii)
iv) increasing for no values of x, decreasing for
b)
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)
b)
c) 1 h and 7 min
d) As his speed increases, the rate of change of his run time decreases.
PTS:
REF:
OBJ:
TOP:
KEY:
1
DIF: 2
Knowledge and Understanding; Application; Communication
Section 3.1
LOC: C2.1, C2.3, C3.7, D1.3, D1.7, D1.9, D2.2
Polynomial and Rational Functions, Characteristics of Functions
word problem, reciprocal of linear function, rate of change, graph