Advanced Functions NAME Review: Exponential & Logarithmic Functions DATE PER

Inverse Functions (4.1)

1) Draw the inverse of the graphs.Label three points on the inverse.

f ( x)

2) Write the inverse function of the function given.

a) f (x) = 3x + 5 b) g (x) =

1 x 2

,2

x ≥ 0

c) d)

3) Prove that the two functions are inverses of each other.

Graphs of Exponential Functions (4.2)

4) What two points are on all base exponential graphs? ________________ and _______________

5) What is the asymptote of all base exponential graphs? __________________

6) Sketch the graph of without a calculator.

-2 -101 2

7) Sketch the graph of without a calculator.

-2 -101 2

8) Explain how to use the graph of to produce the graph of

9) Sketch the graph of without a calculator. Where is the asymptote after the shift?

Logarithmic Functions (4.3)

10) Write the exponential equation in logarithmic form _________________________

11) Write logarithmic equation in exponential form _________________________

12) Evaluate without a calculator. ________________________

13) Evaluate without a calculator. ________________________

14) What is the base of a common logarithm? ___________

15) What is the base of a natural logarithm? ___________

16) Evaluate ________

17) Evaluate ________

Graphs of Logarithmic Functions (4.3)

18) What two points are on all base logarithmic graphs? ________________ and _______________

19) What is the asymptote of all base logarithmic graphs? __________________

20) Sketch the graph of without a calculator.

21) Explain how to use the graph of to produce the graph of

22) Explain how to use the graph of to produce the graph of

y

x

-10

1 5

Properties of Logarithmic Functions (4.4)

23) Use the properties of logarithms to expand the following expressions:

a) b)

24) Use the properties of logarithms to condense the following expressions:

a)

b)

25) Use the change of base formula to rewrite the logarithm as a ratio of logarithms (exact value). Evaluate and

give the approximate value rounded to the thousandth place.

Exact: ________________ Approximate: ______________

Exact: ________________ Approximate: ______________

Solve Exponential and Logarithmic Equations (4.5)

Solve the following exponential equations.. Give answers in exact form and approximate (rounded to the nearest thousandth place) when necessary.

26) x = ____________

27) x = ____________

28) x = ____________

29) x = ____________

State the domain of the following logarithmic functions. Use interval notation.

30) _______________________

31) _______________________

32) _______________________

33) _______________________

Solve the following logarithmic equations. Give answers in exact form and approximate (rounded to the nearest thousandth place) when necessary. If solution is not in the domain, state “no solution.”

34) x = ____________

35) x = ____________

36) x = ____________

37) x = ____________

38) x = ____________

39) x = ____________