Math Questions need help

Please help with these exams. You did the old ones very well, some of the ways you found the solutions were suspicious since it wasn’t covered in the test that way in class. Try your best to answer them by using highschool math as much as you can.

Algebra 2
Unit 6 Exponential & Logarithmic Functions
Directions: Complete the following problems to the best of your ability. Make sure you
show your work. Problems with little to no work shown will result in little to no credit
earned.
1. What is the value of log62? (Yes, you can use a calculator. Round your answer to the
nearest hundredths place)
2. Kyle starts a fundraiser with 43 pennies. He recruits all the players on his
baseball team to participate. His goal is to triple the number of pennies
each day. Assume Kyle meets his daily goal. Use x to represent the number
of days and y to represent the total number of pennies. Write an equation
that represents this scenario.
3. What is the exact value of x in the equation shown below.
𝟓 ∗ 𝟐𝟏𝟓𝒙 = 𝟏𝟔
4. Solve for x in the exponential equation shown below.
𝟓𝟏𝟏𝒙 = 𝟐𝟓(𝒙+𝟗)
5. Looking at each equation listed below, state whether each equation
represents exponential growth or decay. Use a G for growth and a D
for decay in the blank space given to you after each equation listed.
a. 𝒈(𝒙) =
𝟏 𝟒 𝒕
𝟑
( ) _____ b. 𝒇(𝒙) = 𝟎. 𝟖(𝟐. 𝟏)𝒕_____ c. 𝒎(𝒙) = 𝟐 (𝟐)−𝒕
𝟐 𝟑
6. Write the following logarithm in exponential form, as well as the
exponential expression in logarithm form.
a. 𝟓 = 𝒍𝒐𝒈𝟒 𝟔𝟐𝟓
b. 𝟔𝟑 = 𝟐𝟏𝟔
7. Expand the logarithm stated below. You must show each property
used (show your work) to earn full credit.
𝒂𝒎𝟐
𝒍𝒐𝒈 𝟒
𝒃
8. Condense the logarithm stated below. You must show each step you
used to condense to earn full credit.
0.5logm + 0.5logs + 2logd – 3log w
9. Find the inverse of the function stated below.
y=4x – 5
10. Answer the following question. Make sure to show your work!
Directions: Show all necessary work to complete the problems listed below.
Remember I need to see your work to give you maximum amount of credit earned.
1. Divide using polynomial long division.
4𝑥 3 + 6𝑥 2 − 10𝑥 + 4 ÷ 2𝑥 − 1
2. Divide using polynomial synthetic division.
3𝑥 3 + 5𝑥 2 − 11𝑥 + 3 ÷ 𝑥 + 2
3. How many complex roots (zeros) does 𝑓(𝑥) have shown below?
𝑓(𝑥 ) = −3𝑥 3 + 5𝑥 − 2
4. Using the polynomial listed below find the value that is 𝑓(−2).
𝑓 (𝑥 ) = 2𝑥 3 + 5𝑥 2 + 3𝑥 − 7
5. Factor completely over the complex numbers for the polynomial listed
below. (Remember I’m not saying you need this much room, but I’m giving you this much
room just in case – I want you to show your work)
𝑓(𝑥 ) = 𝑥 3 + 𝑥 2 − 22𝑥 − 40
6. Factor the polynomial function listed below over the complex numbers.
𝑓(𝑥 ) = 𝑥 3 + 6𝑥 2 + 11𝑥 + 6
7. Graph the polynomial function below. Make sure you identify your xintercepts, y-intercept, and 2 additional points as well as graph it.
𝑓(𝑥 ) = (𝑥 + 2)(𝑥 − 1)(𝑥 − 3)
Directions: Please complete the following problems to the best of your ability. Make
sure to show as much work possible to support your answers. Problems with little to no
work shown will result in minimum credit earned.
1. Solve the radical equation. Make sure to check for extraneous solutions.
√𝑝 + 6 + 4 = 𝑝
2. Find the restricted domain for the rational expression listed below. Remember you cannot
divide by zero.
3𝑥 − 8
𝑥 2 − 4𝑥 − 12
3. Simplify the rational expression listed below. Factoring helps.
𝑥 3 − 𝑥 2 − 42𝑥
2𝑥 2 − 20𝑥 + 42
4. Multiply the two rational expressions listed below. Make sure your answer is as
simplified as possible.
45𝑥 2 𝑥 2 − 5𝑥 − 36
∙
𝑥 − 9 3𝑥 2 + 12𝑥 2
5. Simplify the complex fraction below. Make sure your answer is as simplified as
possible.
9
𝑥
9
2
+
𝑥 3𝑥
6. Subtract the two rational expressions listed below. Make sure your answer is as
simplified as possible.
4𝑥
𝑥
−
𝑥 2 + 𝑥 − 20 𝑥 2 − 8𝑥 + 16
7. Add the two rational expressions listed below. Make sure your answer is as simplified as
possible.
3
𝑚
+ 2
𝑚 + 5 𝑚 + 7𝑚 + 10
8. Solve the rational equation below. Make sure you check and identify any extraneous
solution(s). Make sure to show your work.
1
1
𝑥−2
+
=
𝑥 𝑥−3
𝑥−3