Microsoft Word - Review Ch 4. Exp and Log Functions2.docx 4 te… · Web viewMicrosoft Word -...
Transcript of Microsoft Word - Review Ch 4. Exp and Log Functions2.docx 4 te… · Web viewMicrosoft Word -...
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.
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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 = ____________