University of Toronto Exponents Logarithmic & Trigonometric Functions Questions

Only accept if you are available to help me for the next 3 hours solving a math assignment I would need you to solve each question and send it to me one after the other there should be no more than 18 high school grade questions from the topics of Basic Fundamentals, Functions, Polynomial and Rational Functions, Exponents and Logarithmic Functions and Trigonometric functions I’ll be attaching previous few quizzes in chat to explain a little more but Ill need you to be with me for next at least 3 hours.

ASSIGNMENT- 1
[5]
[3]
3x − 1
1. (a) Solve the inequality −2 ≤
≤ 7. Graph the solution set
5
and
write it in the interval notation.
(b) Find the domain of the function f (x)= √
swer in interval notation.
[3]
[4]
−2 − x
. Write the an-
7
x
2. (a) Determine algebraically if the following function is even, odd, or
neither.
5
3
f (x) = 3x + x − x
x4 +1
(b)
Given f (x) = x2 − 5 and g(x) = x + 3,find (f ◦ g)(−2).
Page 1 of 6
[6]
[4]
[4]
[4]
3. Graph the function f (x) = −(x − 1)3 using transformations. Find the
domain and range of the function using the graph of the function.
4. Find all the asymptotes,
if they exist for the rational function:
x2 − x + 6
.
R(x) =
2×2 + 3x − 2
5. (a) Simplify:
x−2 − y−2
x−1 + y−1
(b) Solve for x:
2 + 5 =
3 .
2
x − 9 x − 3 x +3
Page 2 of 6
[3]
[5]
2×4 + x3 − x + 4
x −2
and remainder.
6. Divide
using Synthetic Division. Find the quotient
7. The piecewise function f (x) is given below:
. 2
3x − 2x
x≤1
f (x) = x − 4
x>1
(a) Evaluate: f (−1), f (4)
(b) Graph f (x).
(c) Is this piecewise function continuous? If it is not continuous, state
why.
Page 3 of 6
[8]
8. Given a quadractic function f (x) = 2×2 + 4x + 2.
(a)Express f in the standard form.
(b) Find the vertex and x and y-intercepts of f .
(c) Sketch the graph.
(d) Find the maximum or minimum value of the function f .
Page 4 of 6
[8]
9. Consider the polynomial function P (x) = (x + 2)(x + 1)2(2x − 1).
(a) Identify the real zeros, their multiplicity, and whether the
function Touches (T) or Crosses (C) the x axis using the table
below:
ZEROS
MULTIPLICITY
T or C
(b) Find the y intercept.
(c) Determine the maximum possible number of turning points for P (x).
(d) Graph P (x) and label the x intercepts on the graph.
Page 5 of 6
Bonus
[2]
[2]
10. (a) Find the equation of the circle centered at (3,−4) and passes through
(5, 2).
x−3
.
(b) Find the inverse of the function f (x) =
2x + 1
[57 + 4 BONUS]
Page 6 of 6
ASSIGNMENT- 2
1. Use the properties of logarithms to find the exact value of each of the
following expressions:
[1]
(a) e2ln7
[1]
(b) 3log314
[3]
[3]
[4]
√
(c) log9 3
(d)
log2 16
log2 8
2. (a) Write the expression as a sum and/or difference of the logarithms
using laws of logarithms.
2
(x − 5)
ln √ 2
x +1
2
3
Page 1 of 5
[4]
[6]
(b) Solve the following logarithmic equation.
log6(x + 4) + log6(x + 3) = 1
3. Using transformation(s), draw the graph of f (x) = 2+log2(x − 3). Find
the domain and range of f (x). Also label any asymptote(s) on the graph.
Page 2 of 5
4. Solve the following exponential equations:
1
343
[4]
(a) 72x−1 =
[4]
(b) 41−x = 32x+5
[6]
4
5. Given sin θ = − , and θ lies in third quadrant. Find the remaining 5
7
trigonometric functions. Rationalize all denominators.
Page 3 of 5
6. Find the exact value of the trigonometric function given below:
[2]
(a) sec (405◦)
[3]
(b) tan −
[3]
(c) csc
[2]
(d) csc2 62◦ −
[5]
π
3
19π
3
+ 2 tan
π
6
cos2 62◦
sin2 62◦
7. Given f (x) = −3 cos (x), find the amplitude and the period and then
give a rough sketch of the graph of f (x).
Label BOTH the amplitude and period length on the graph.
Page 4 of 5
[4]
BonUs
8. Find the inverse of the exponential function y = ex−2 + 3.
[51
+ 4 BonUs]
Page 5 of 5
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Q1 (9 points)
高三
a) [2 points] Determine algebraically if the following function is even, odd, or neither.
f(0) = -26
+ 2.24
522
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b) [4 points] Solve the inequality 17x + 4 > 10. Graph the solution set and write it in the interval notation.
c) [3 points] Given f(x) = 3+24 and g(x) = VI – 5, find (gof)(2)
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Q2 (6 points)
a) [3 points] Simplify:
73
3-3 -9
3
2
b) [3 points] Simplify:
– 6
2 – 5
6
+
C 5 – 2
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Q3 (8 points)
Use the properties of logarithms to find the exact value of each of the following expressions:
e
a) [2 points) In
(5)
3 On-Screen Keyboard
Х
b) (1 point] log4 4-5
Esc
x
c) [3 points] 2 log, 27
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7
i
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q
w
e
t
у
u
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Del
End
[.
Mv Up
d) [2 points] 2log, 6-log, 7
1
Enter
a
S
d
f
g
hj
k
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:
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Caps
Shift
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Q18 (6 points)
1 2 3 4 5 6 7
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Find the exact value of the following trigonometric functions.
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qwertyui
орг
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End
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a) [3 points] sin 75° by using Addition or Subtraction formula only.
“. Enter
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Capsa s d f g h j k |
Shift z xcvbnm
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b) [3 points] cos 67.5° by using the Half-Angle formula only
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Q19 (8 points)
a) [5 points] Solve the basic trigonometric equation 3V2 sin ( +2 = -1 and list any four solutions.
b) [3 points] Using trigonometric identities, solve the trigonometric equation: 2 cos? – sin 0 = 1 in the interval [0, 0).
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Before you submit, please ensure that your pages are in order and rotated correctly.
Note: You will not be able to resubmit your work after the due date has passed.
Submit for evaluation
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Q5 (8 points)
a) [3 points] Find a point on y-axis that is equidistant from the points (2, -3) and (-4,5).
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b) [3 points] Find the equation of the line passing through the points (-6,1) with a slope –
8
Math Access II (MATH-0042-0…
c) [2 points] Draw the inverse of the graph given in the diagram below:
On-Screen Keyboard
X
6
1 2 3 4 5 6 7
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qwertyui
орг
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(-4, 2)
2
(-2,1)
-8
-6
4
-2
0
2
4
6
8
(0, -2)
(4, -3)
-6
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Q4 (9 points)
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Find the exact value of the trigonometric functions given below:
a) [3 points] 4(cos 30° + tan 60°)
Math Access II (MATH-0042-0…
b) [3 points] tan
– cos(-1)
On-Screen Keyboard
X
(1950
235)
c) [3 points) CSC
1 2 3 4 5 6 7
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Q5 (8 points)
a) [3 points] Find a point on y-axis that is equidistant from the points (2, -3) and (-4,5).
3
b) [3 points) Find the equation of the line passing through the points (-6,1) with a slope –
8
c) [2 points] Draw the inverse of the graph given in the diagram below:
-6
(-4, 2)
2
(-2,1)
-8
-6
-4
-2
2
4
6
8
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Q6 (6 points)
Solve the following exponential equations:
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a) [3 points] 572.543
1
125
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b) [3 points] el-3x = 9
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1 2 3 4 5 6 7
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Q7 (6 points)
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The piecewise function f(x) is given below:
– 3