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.

๐ โ ๐๐๐๐ = ๐๐

4. Solve for x in the exponential equation shown below.

๐๐๐๐ = ๐๐(๐+๐)

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. ๐(๐) =

๐ ๐ ๐

๐

( ) _____ b. ๐(๐) = ๐. ๐(๐. ๐)๐_____ c. ๐(๐) = ๐ (๐)โ๐

๐ ๐

6. Write the following logarithm in exponential form, as well as the

exponential expression in logarithm form.

a. ๐ = ๐๐๐๐ ๐๐๐

b. ๐๐ = ๐๐๐

7. Expand the logarithm stated below. You must show each property

used (show your work) to earn full credit.

๐๐๐

๐๐๐ ๐

๐

8. Condense the logarithm stated below. You must show each step you

used to condense to earn full credit.

0.5logm + 0.5logs + 2logd โ 3log w

9. Find the inverse of the function stated below.

y=4x โ 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.

4๐ฅ 3 + 6๐ฅ 2 โ 10๐ฅ + 4 รท 2๐ฅ โ 1

2. Divide using polynomial synthetic division.

3๐ฅ 3 + 5๐ฅ 2 โ 11๐ฅ + 3 รท ๐ฅ + 2

3. How many complex roots (zeros) does ๐(๐ฅ) have shown below?

๐(๐ฅ ) = โ3๐ฅ 3 + 5๐ฅ โ 2

4. Using the polynomial listed below find the value that is ๐(โ2).

๐ (๐ฅ ) = 2๐ฅ 3 + 5๐ฅ 2 + 3๐ฅ โ 7

5. Factor completely over the complex numbers for the polynomial listed

below. (Remember Iโm not saying you need this much room, but Iโm giving you this much

room just in case โ I want you to show your work)

๐(๐ฅ ) = ๐ฅ 3 + ๐ฅ 2 โ 22๐ฅ โ 40

6. Factor the polynomial function listed below over the complex numbers.

๐(๐ฅ ) = ๐ฅ 3 + 6๐ฅ 2 + 11๐ฅ + 6

7. Graph the polynomial function below. Make sure you identify your xintercepts, y-intercept, and 2 additional points as well as graph it.

๐(๐ฅ ) = (๐ฅ + 2)(๐ฅ โ 1)(๐ฅ โ 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.

โ๐ + 6 + 4 = ๐

2. Find the restricted domain for the rational expression listed below. Remember you cannot

divide by zero.

3๐ฅ โ 8

๐ฅ 2 โ 4๐ฅ โ 12

3. Simplify the rational expression listed below. Factoring helps.

๐ฅ 3 โ ๐ฅ 2 โ 42๐ฅ

2๐ฅ 2 โ 20๐ฅ + 42

4. Multiply the two rational expressions listed below. Make sure your answer is as

simplified as possible.

45๐ฅ 2 ๐ฅ 2 โ 5๐ฅ โ 36

โ

๐ฅ โ 9 3๐ฅ 2 + 12๐ฅ 2

5. Simplify the complex fraction below. Make sure your answer is as simplified as

possible.

9

๐ฅ

9

2

+

๐ฅ 3๐ฅ

6. Subtract the two rational expressions listed below. Make sure your answer is as

simplified as possible.

4๐ฅ

๐ฅ

โ

๐ฅ 2 + ๐ฅ โ 20 ๐ฅ 2 โ 8๐ฅ + 16

7. Add the two rational expressions listed below. Make sure your answer is as simplified as

possible.

3

๐

+ 2

๐ + 5 ๐ + 7๐ + 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

๐ฅโ2

+

=

๐ฅ ๐ฅโ3

๐ฅโ3