Advanced Algebra with Trig

Advanced Functions and Modeling NAME ______

Final Exam Review: 2013 DATE ______PER ______

• This packet is due on or before Friday, May 24, 2013by 3:50 pmin my handwith no exceptions. If you will be out, then

you need to have a trusted friend or parent bring me the packet. Show all work to earn credit.

• This is a 25-point grade: 5 points based on completion and 4-points each for accuracy on 5 randomly selected problems.
• One point will be deducted for each problem not completed or without work.
• You will be able to make corrections between the day of the review and the day of the exam. On the day of the exam, you will turn the packet to be graded for accuracy.

Your work/process is worth points so you must show it to earn full credit.

1) Determine if the inverse of the function is also a function. Explain why.

a) b)

2) Draw the inverse of the graph. Label three points on the inverse.

3) Write the inverse function of the function given:

4) Use composition to prove the two functions are inverses of each other.

Graphs of Exponential Functions:

5) Sketch the graph of without a calculator.

x /
0
1
2

6) Sketch the graph of without a calculator. HINT: Graph first.

x /
0
1
2

7) Explain how to use the graph of to produce the graph of .

8) What two points are on all base exponential graphs?

9) What is the asymptote of all exponential graphs that have no shift?

Rewriting Exponential and Logarithmic Functions:

10) Write in exponential form.

11) Evaluate without a calculator.

Graphs of Logarithmic Functions:

12) Sketch the graph of without a calculator.

13) Identify the equation represented by the graph. Hint: It can be written as a logarithm.

14) Explain how to use the graph of to produce the graph of .

15) What two points are on all base logarithmic graphs?

16) What is the vertical asymptote of all logarithmic graphs that have no shift?

Properties of Logarithmic Functions:

17) Use the properties of logarithms to condense .

18) Use the properties of logarithms to expand .

19) Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.

20) What is the base of a common logarithm?

21) What is the base of a natural logarithm?

22) Evaluate .

23) Evaluate .

24) Find the value of without using a calculator.

25) Find the value of without using a calculator.

26) Solve for x without using a calculator.

27) Solve for x without using a calculator.

28) Solve for x without using a calculator.

Finding the Domain of Logarithmic Functions:

29) Find the domain of .

DOMAIN: ______

30) Find the domain of .

DOMAIN: ______

Solving Logarithmic Functions:

31) Solve for x without using a calculator.DOMAIN: ______

Solution: ______

32) Solve for x without using a calculator.DOMAIN: ______

Solution: ______

33) Solve for x without using a calculator.

Solution: ______

34) Solve for x without using a calculator.

Solution: ______

Using a Calculator to Evaluate:

35) Evaluate using a calculator. Round the result to three decimal places.

36) Evaluate using a calculator. Round the result to three decimal places.

37) Use the change-of-base formula to evaluate . Round the result to three decimal places.

Solving Equations:

38) Solve for x. Find the EXACT answer, then round the result to three decimal places.

Solution: ______

39) Solve for x. Find the EXACT answer, then round the result to three decimal places.

DOMAIN: ______

Solution: ______

40) Mr. Poland won $5000 for being 1st runner up at the World’s Strongest Man contest. He invested his

entire winnings at 4.5% interest.

a)Does this problem represent exponential growth or decay? ______

b)Write an exponential equation describing the situation ______

c)How much money will he have in 10 years? (Show work)______

d)How many years will it take for him to have $7500? ______

(Show work by solving an equation. Round your result to the nearest tenth and give proper units)

41) After a race, a runner’s pulse rate R in beats per minute decreases according to the function

, where t is measured in minutes.

______a) Find the runner’s pulse rate at the end of the race.

______b) How long, to the nearest minutes, after the end of the race will the runner’s

pulse rate be 100 beats per minute?

Trigonometry Review. No decimal answers!!

42) State the definition of an angle in standard position.

43) Find a positive angle that is coterminal with an angle measuring .

44) If an angle in standard position measures radians, in which quadrant does its terminal side lie?

45) Find an angle that is complementary with an angle measuring .

46) Find an angle that is supplementary with an angle measuring .

47) Convert radians to degree measure.

48) Convert to radian measure.

49) Find the EXACT value of without using a calculator. Show your angle and coordinates.

50) Find the EXACT value of without using a calculator. Show your angle and coordinates.

51) Suppose and the terminal side of the angle lies in Quadrant III, find .

52) Suppose and the terminal side of the angle lies in Quadrant III, find .

53) Suppose and the terminal side of the angle lies in Quadrant IV, find .

54) Suppose and , find .

55) Let be an acute angle of a right triangle for which . Find the EXACT value of .

56) Find the reference angle for an angle measuring .

57) Change to radian measure. Round to the nearest thousandth.

58) Find the EXACT (no decimals) value of .

59) Find the EXACT value of .

60) Find the value of for the angle whose terminal side passes through the point .

61) Use right triangle ABC to find measure of angle B, and sides a and c.

Round to the nearest tenth.Remember to label the diagram, write out the trigonometric equation, write

the substitutions, and write all calculator values before rounding the final answers.

62) Use right triangle ABC to find measure of angles A & B and side c.

Round to the nearest tenth.Remember to label the diagram, write out the trigonometric equation

write the substitutions, and write all calculator values before rounding the final answers.

63) From a point 35 feet from the bottom of a oak tree, the angle of elevation to the top of the tree

is . Find the height of the tree to the nearest foot.

64) Let be an angle in standard position. State the quadrant in which the terminal side of lies.

,

65) An observer notes that the angle of elevation from point A to the top of a U.S. Capitol is .

From a point 100 feet further from away, the angle of elevation is . To the nearest foot, find

the height of the U.S. Capitol.