**Unformatted text preview: **Unit Test 2
Course: Advanced Functions 12, MHF4U
Date: ………….………..
Time: …… hours +
Name: _____________________________________ Examination Marks Breakdown
Knowledge: 12
Application: 16
Communication: 10
Inquiry/Thinking: 5
Total Marks:
/ 43
Short Answers:[ /
, Long Answers:[ 1.
2.
3.
4.
5. /
, Total:[ / Give EXACT answers for all questions unless otherwise indicated.
Neat, complete solutions are required.
Read all questions carefully.
For full marks, correct mathematical form is necessary.
You are NOT allowed any books, or electronic devices in the exam (No textbooks,
dictionaries, cell phones, ipods, mp3 players)
6. You are allowed to bring a calculator, ruler, high-lighters, white-out and pens.
7. Write your exam in pen.
8. You have 2 hours to complete the exam. Please sign here prior to the start: Short Answers:
Answer each question in their designated area: Show your work for every question:
1) Express that if the following statement is true or false. Write the complete right answer for each
question: (4 Marks, K:2, A:2) The function has only one vertical asymptote at x = –5 . 2 + 9 + 20 = 0, ( + 5)( + 4) = 0, 2. What is true about the function
C:1) ℎ = −5 = −4 . Explain the end behaviour ? (3 Marks, T:2, 3
+ 1 = −(0+ ) + 1 = 0− + 1 = +1−
→+∞
∞−3
3 → −∞, ℎ lim () = −
+ 1 = −(0− ) + 1 = 0+ + 1 = +1+
→−∞
−∞ − 3 → +∞, ℎ lim () = − 3. Which of the following is true? (2 Mark, K:1, T:1) .
4. The horizontal asymptote of the function is : (1 Mark, K:1) . ℎ ℎ ℎ . , 12
=4
3 (2
Mark,
K:1,
T:1) 1 − = 0, ℎ(0) =
2
4
4
1
. (0) = −
=−
=
(0)2 − 7(0) − 8
−8 2
6. Based on the form of the rational function, how can you identify the vertical, horizontal or
oblique asymptotes, or no asymptotes? (4 Mark, T:1, C:3) + = 0, + ≠ 0,
ℎ () = ±∞ ℎ . =− → ±∞ () = ,
ℎ ℎ ℎ .
() = ℎ ℎ:
ℎ ℎ 1 ℎ ℎ ℎ . ℎ ℎ + + ℎ ℎ:
ℎ ℎ ℎ 1 ℎ ℎ ℎ Long Answers:
Answer each question in their designated area:
1) Solve, 0 , algebraically and show your work. (6 Mark, K:2, A:4) +3
≥0
+1 + 1 = 0, ℎ = −1, () = ( ) + 3 = 0, ℎ = −3, () = 0 () + ℎ ≥ 0, :
(−∞, −3] ∪ (−1, +∞) −3
0 − −1 + 2)Draw a labeled sketch for a rational function with the following conditions. (6 Marks, K:2, C:2, A:2)
● is a reciprocal of a linear function
● horizontal asymptote is y = 0
● vertical asymptote is x = 1
● y-intercept is -1/2
● only has intervals of decrease = 1, ℎ ℎ ( − 1) = 0, ℎ lim () = 0
→∞
1
1 − − , ℎ(0) = −
2
2
1
() =
2( − 1) 3) for the function find the following: (6 Marks, K:2, A:4) a) Domain and Range
Domain:
1 1 2 2 2 − 1 = 0, ℎ = , + 1 = 0, ℎ = −1, : − {−1, }
Range: : (−∞, − 16 ∪ (0, +∞)
9 b) X, and y intercept (0) = 2 = 2
= −2, − (0, −2)
(−1)(1) (2(0) − 1)((0) + 1)
2
() = 0,
= 0, , − (2 − 1)( + 1) c) Vertical and horizontal asymptote : lim () = 0+ , lim () = 0+ ,
→+∞ →−∞ : lim + () = +∞, lim − () = −∞,
→+ 1
2 lim () = −∞, →−1+ d) Graph the function 1
→+
2 lim () = +∞, →−1− 4) Explain what rational functions are. How many types of rational functions have we learnt in chapter 3.
Bring 3 examples for every case and show them by writing the formula and graph them. (5 Marks, K:1,
C:4) Any function that is defined by rational fraction is rational function. (−3)(+4)
5) Solve
(−1) = (+3)(2+6)
(4 Marks, A:4)
(+5) ( − 3)( + 4) ( + 3)(2)( + 3)
=
( − 1)
( + 5)
( − 3)( + 4) (2)( + 3)2
=
( − 1)
( + 5)
( 2 + − 12)( + 5) = (2)( 2 + 6 + 9)( − 1)
( 3 + 6 2 − 7 − 60) = (2 3 + 10 2 + 6 − 18)
( 3 + 4 2 + 13 + 42) = 0 ≈ −3.6166 Communication Rubric:
Achieveme Level 0
nt
0-49%
Category Level 1
50-59% Level 2
60-69% Level 3
70-79% Level 4
80-100% Knowledge No
/
evidence
Understan
ding Shows a
limited
understandin
g of the
concepts Shows some
understandin
g of the
concepts Shows an
understandin
g of the
concepts Shows a high
degree of
understanding
of the
concepts Applicatio
n No
evidence Shows a
limited
connection
between
trigonometry
and
profession. Shows some
understandin
g of the
scenario and
answers few
questions Shows a clear
understandin
g the scenario
and
calculating
the problems Shows a good
understanding
of the problem
and solved the
questions Communic
ation No
evidence Report &
presentation
shows
limited clarity Report &
presentation
shows some
clarity Report &
presentation
shows clarity Report &
presentation
shows a high
degree of
clarity ...

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- Fall '19
- lim, Rational function