Jungshik Shin F2021UPG101-093
Final Exam is due on Tuesday, December 07, 2021 at 12:00pm.
The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your e
or, you
should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help.
There are also other resources at your disposal, such as the Mathematics Continuous Tutorials. Don’t spend a lot of time guessing – it’s
not very efficient or effective.
Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2, (2+
tan(3))∗ (4− sin(5))∧6−7/8 instead of XXXXXXXXXX, etc.
Problem 1. (1 point)
Which of the following graphs represents a relationship where y
is a function of x?
Note: You can click on the graph for a larger view.
• A
• B
• C
• D
• E
• F
Answer(s) submitted:
•
(inco
ect)
1
Problem 2. (1 point)
In the following graph, y = f (x) is illustrated in blue and y = g(x)
is illustrated in green.
Evaluate ( f −g)(0).
• −1
• 0
• 1
• 2
• 3
• 4
Answer(s) submitted:
•
(inco
ect)
Problem 3. (1 point)
f (x) = x3−9x2 +27x−21.
The inverse function is f−1(x) = . . .
• 3
√
x+6−3
• −1x3−9x2+27x−21
• 3
√
x−6+3
• 3
√
x−6−3
• 1x3−9x2+27x−21
• 3
√
x+6+3
Answer(s) submitted:
•
(inco
ect)
2
Problem 4. (1 point)
f (x) =
2x−3 if x≤ 0
1 if 0 < x < 3
x2 +3 if x≥ 3
.
Evaluate f (3).
• −3,1,12
• −3,1
• −3
• 1
• 1,12
• 12
Answer(s) submitted:
•
(inco
ect)
Problem 5. (1 point)
Consider the point P = (−10,0) on the graph of y = f (x).
Find the point co
esponding to P on the graph of y =−5 f
(
2(x+
4)
)
−2.
• (−4,−2)
• (−4,48)
• (−9,48)
• (−10,48)
• (−10,−2)
• (−9,−2)
Answer(s) submitted:
•
(inco
ect)
Problem 6. (1 point)
The function y = f (x) illustrated below has neither even nor odd
symmetry.
Determine which of the following shifted functions of f has odd
symmetry.
• f (x+3)+1
• f (x+5)+1
• f (x+1)−6
• f (x+5)−6
• f (x+1)+8
• f (x+3)+8
Answer(s) submitted:
•
(inco
ect)
3
Problem 7. (1 point)
Determine the equation of the ellipse that is illustrated in the graph
elow.
• (x−1)
2
6 +
(y+2)2
2 = 1
• (x−1)
2
4 +
(y+2)2
36 = 1
• (x−1)
2
36 +
(y−2)2
4 = 1
• (x−1)
2
2 +
(y+2)2
6 = 1
• (x−1)
2
4 +
(y−2)2
36 = 1
• (x−1)
2
36 +
(y+2)2
4 = 1
Answer(s) submitted:
•
(inco
ect)
Problem 8. (1 point)
Consider the function f (x) =
16x8 +bx6 +4
4x6 + cx5 +4
where b and c are
eal numbers.
If you set up long division, what is the first term A across the top?
• A = 4x
• A = 16x2
• A = 64x14
• A = 16x3
• A = 1
• A = 4x2
Answer(s) submitted:
•
(inco
ect)
Problem 9. (1 point)
f (x) = 15x4 +Ax3 +Bx2 +Cx+25, where A,B,C are integers.
The list of all potential rational zeroes of f (x) is:
• ±{1,3,5,15, 15 ,
3
5 ,
1
25 ,
3
25}
• ±{1,5,25, 15 ,
1
3 ,
5
3 ,
25
3 ,
1
15}
• ±{1,5,25}
• ±{1,3,5,15,25}
• ±{1,3,5,15}
• ±{1,5,25, 15 ,
1
3 ,
1
15}
Answer(s) submitted:
•
(inco
ect)
4
Problem XXXXXXXXXXpoint)
Consider the following set: (−∞,−4)∪ (1,3)∪ (3,∞).
Which of the following inequalities has this set as its solution?
• (x+4)5(x−1)5(x−3)3 > 0
• (x+4)6(x−1)4(x−3)7 > 0
• (x+4)5(x−1)5(x−3)2 > 0
• (x+4)3(x−1)4(x−3)4 > 0
• (x+4)4(x−1)2(x−3)6 > 0
• (x+4)7(x−1)4(x−3)5 > 0
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Suppose that a<
c. The graph of y= f (x) is illustrated below.
Which of the following functions best describes f (x)?
• f (x) = (x−a)2(x−b)(x− c)
• f (x) = (x−a)(x−b)2(x− c)
• f (x) = (x−a)(x−b)(x− c)2
• f (x) = (x−a)2(x−b)2(x− c)
• f (x) = (x−a)2(x−b)(x− c)2
• f (x) = (x−a)(x−b)2(x− c)2
Answer(s) submitted:
•
(inco
ect)
5
Problem XXXXXXXXXXpoint)
Consider the rational function f (x) = x
2+ax+
x2+cx+d .
Suppose that the graph y = f (x) has zeroes at x = −1 and x = 6
and vertical asymptotes at x =−2 and x = 5. Find the y-intercept.
• f (0) = 65
• f (0) =−6
• f (0) =−10
• f (0) = 53
• f (0) = 35
• f (0) = 12
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Simplify the following:
(
3x4y5
)4
• 81x8y9
• 81x16y20
• 12x8y9
• 12x16y20
• 12x256y625
• 81x256y625
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
The following graph represents an exponential function of the
form f (x) = Aebx + k.
What is the value of k?
• k =−3
• k =−2
• k =−1
• k = 1
• k = 2
• k = 3
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Find the domain of the following logarithmic function:
f (x) = log9(4−9x).
• x > 4
• x < 49
• x > 49
• x < 0
• x > 0
• x < 4
Answer(s) submitted:
•
(inco
ect)
6
Problem XXXXXXXXXXpoint)
Expand and simplify the following logarithm: log2
(
32(A+1)5
B4C4
)
• 32+5log2(A+1)−4log2 B−4log2 C
• 5+5log2(A+1)−4log2 B+4log2 C
• 32+5log2(A+1)−4log2 B+4log2 C
• 16+5log2(A+1)−4log2 B−4log2 C
• 16+5log2(A+1)−4log2 B+4log2 C
• 5+5log2(A+1)−4log2 B−4log2 C
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Consider the following logarithmic equation:
log2(x+4)+ log2(x+8) = 5.
When solving the equation, which of the following would be
equivalent:
• (x+4)+(x+8) = 10
• (x+4)(x+8) = 25
• (x+4)+(x+8) = 25
• (x+4)+(x+8) = 32
• (x+4)(x+8) = 32
• (x+4)(x+8) = 10
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
A radioactive substance initially has a mass of 820 grams. After 9
seconds, the mass has reduced to 664 grams.
Assuming exponential decay, we can model the mass (in grams)
of the substance after t seconds by M(t) = . . .
• 820e−0.07688t
• 820e0.02345t
• 820e0.07688t
• 820e−0.02345t
• 820e−0.21102t
• 820e0.21102t
Answer(s) submitted:
•
(inco
ect)
7
Problem XXXXXXXXXXpoint)
Find the measure of angle A, to the nearest tenth.
• A = 57.1◦
• A = 32.9◦
• A = 40.4◦
• A = 49.6◦
• A = 122.9◦
• A = 139.6◦
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
sin(A) = − XXXXXXXXXX .
If A is in quadrant 4, find the exact value of tan(A):
• − XXXXXXXXXX
• −3832000
• − XXXXXXXXXX
• XXXXXXXXXX
• XXXXXXXXXX
• XXXXXXXXXX
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Consider the graph of the function f (x) = 16sin(bx + c) + 17,
where b and c are real constants.
What is the range of y = f (x)? In other words, what is the set of
possible y-values?
• (−1,33)
• [0,16]
• [−1,33]
• [1,33]
• (0,16)
• (1,33)
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Find the length of the side x in the following illustration, co
ect
to two decimal places:
Note that the illustration is “mostly” to scale and there are no in-
dicated right-angles.
• x = 60.24
• x = 76.26
• x = 43.59
• x = 32.99
• x = 73.19
• x = 41.07
Answer(s) submitted:
•
(inco
ect)
8
Problem XXXXXXXXXXpoint)
The graph of a trigonometric function y = f (x) is illustrated in
lue below: Using the graph, find all solutions in R to f (x) = 4.
• x = 2+2k,4+2k for all k in Z
• x = 4+5k for all k in Z
• x = 2+3.5k for all k in Z
• x = 2+5k,4+5k for all k in Z
• x = 2+2k for all k in Z
• x = 2+7k,4+7k for all k in Z
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Evaluate arccos
(
−
√
3
2
)
in degrees.
• A =−60◦
• A =−45◦
• A =−30◦
• A = 120◦
• A = 135◦
• A = 150◦
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Consider the trigometric expression: 1−sin(x)cos(x) .
Using trigonometric identities, this expression is equivalent to:
• sin(x) tan(x)
• sec2(x)
• sin(x)− cos(x)
• sec(x)− tan(x)
• 1−cos(x)sin(x)
• cos2(x)
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Angles A and B are both in the first quadrant (in the interval [0, π2 )).
Given sin(A) = XXXXXXXXXXand tan(B) =
8
15 , evaluate cos(A−B).
• XXXXXXXXXX
• XXXXXXXXXX
• −8972465
• XXXXXXXXXX
• −8962465
• −8982465
Answer(s) submitted:
•
(inco
ect)
9
Problem XXXXXXXXXXpoint)
Evaluate the following: 108!105! .
• XXXXXXXXXX
• XXXXXXXXXX
• 11664
• 11340
• 11556
• XXXXXXXXXX
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Jeremiah wants to decorate his laptop with a row of stickers across
the top. He has 11 distinct stickers to choose from for this task.
His favourite numbers are 2 and 6 so he will decorate his laptop
with a row of with either 2 or 6 stickers.
How many different ways could he a
ange the stickers?
• XXXXXXXXXX
• 332640
• 332750
• 517
• 110
• XXXXXXXXXX
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
Brent’s Restaurant sells poke bowls. In a MEGA-bowl, you can
choose
• a base of either spinach or rice
• 2 different proteins of either tuna, salmon, scallop, tofu, o
chicken
• 2 different fillers from a selection of 6
• 4 different toppings from a selection of 6
How many different MEGA-bowls of poke can you make?
• 432000
• 19
• 412
• 42
• 4500
• 360
Answer(s) submitted:
•
(inco
ect)
Problem XXXXXXXXXXpoint)
In the expanded and simplified expression of f (x) = (3x4−5)14,
find the x44 term.
• 8060188500x44
• −177147x44
• −8060188500x44
• 479882812500x44
• −479882812500x44
• 177147x44
Answer(s) submitted:
•
(inco
ect)
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10
Jungshik Shin F2021UPG101-093
Final Exam is due on Tuesday, December 07, 2021 at 12:00pm.
The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your e
or, you
should consult the textbook, or ask a fellow student, one of