# Great Lakes Christian College Exponential and Logarithmic Form Exercises

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I am looking for a tutor who has good foundation in the following topics (Polynomial and rational functions, Exponential logarithmic functions) to take of the following assignments using the rubric system provided.

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TVO ILC
MHF4U – Unit 1
Unit 1 Assessment, Part 1
Unit 1 Assessment, Part 1
1. Fill in the tables below for each of the following polynomials: [K10]
a)
3
f​(​ x)​=​−  ​  _14 ​  x​​  ​− 13 ​x​​  2​+ 3x − 9​
Degree
b)  ​f​(x)​=​6x​​  4​
Degree
Type of
polynomial
coefficient
End behaviours
Domain
coefficient
End behaviours
Domain
+​7x​​  2​ − 8x + 9​
Type of
polynomial
1
TVO ILC
MHF4U – Unit 1
Unit 1 Assessment, Part 1
2. Fill in the table below for the polynomial function: [K9]
​f​(x)​= −  ​ (​​x− 4​)​​ ​​(x+ 1)​​​  2​​(​​x− 5​)​​​​
​x –​ intercepts
​y − ​ intercept
End behaviours
and behaviour of graph at
each ​x − ​intercept
Sketch:
2
TVO ILC
MHF4U – Unit 1
Unit 1 Assessment, Part 1
3. Solve the following equation algebraically. Explain your process. [A6], [C3]
​0 = 18 ​x​​  4​+ 87 ​x​​  3​+ 3 ​x​​  2​− 108x​
4.
a) Describe the transformations on the cubic function below.

f​(x)​= 7 ​​[1_2​ ​​(x− 5)​]​​​  3​− 45​
b) The point (-9, -2446) is on the transformed function ​f​(x)​= 7 ​​[1_​2​​(x− 5)​]​​​  3​− 45​use the
transformation statement the find the original point on the parent function. Justify your
3
TVO ILC
MHF4U – Unit 1
Unit 1 Assessment, Part 1
5. Determine the values of ​m​and ​n ​for ​ f​(x)​= mx​​  3​+ 20​x​​  2​+ nx​− 35​given that ​​
(x+ 1)​ gives a remainder of zero, and when divided by ​​​(x− 2)​the remainder is 45. [T5],
[C3]
6. Use algebra to determine whether the following function is even, odd or neither. [A6]
a)
​f​(x)​= 55 ​x​​  4​−​x​​  2​− 78​
b)
f(x)=37×3+93x
4
MHF4U – Unit 1
TVO ILC
Unit 1 Assessment, Part 2
Unit 1 Assessment, Part 2
1. Use the characteristics of the given function to graph the function and it’s reciprocal on
the same set of axes, either using online graphing technology or by hand. State the
intercepts and identify any maximum or minimum points, where possible. Explain
​f​(x)​  = ​− x​​  2​+ 7x – 6​
1
MHF4U – Unit 1
TVO ILC
Unit 1 Assessment, Part 2
2. a. Fill in the table and sketch the graph of the following equation. [A10], [C2]
-2x – 5

​f(​ x) =​ _
3x + 18 ​​
Vertical
asymptotes
Horizontal
asymptotes
x​ − ​ intercept
​y− ​intercept
Domain
2
MHF4U – Unit 1
TVO ILC
Unit 1 Assessment, Part 2

2x− 5 ​ [K2]
2 b. State positive and negative intervals for ​f​(x)=
​ −
​____________
3x+ 18
Positive interval:
Negative intervals:
3. Find the real roots of the following rational equations. [K8] [C2]
_
− 7x
a. 9x
​  + 11 ​− 12= x_1

b.
___
​​  x–1​​ = ____
​​ 3x+8​​
x+2 5x–1
4. Solve the following inequality algebraically. Explain your process. [A4] [C2]
​8x − 3 ≤ 2x + 1 ≤ 17x – 8​
3
MHF4U – Unit 1
TVO ILC
Unit 1 Assessment, Part 2
5. S
olve the following inequality algebraically. Include an interval chart in your solution.
[A6] [C2]
​​
____
​​ 5x+4

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