1. The inverse of every logarithmic function is an exponential function and vice-versa. What does this tell us about the relationship between the coordinates of the points on the graphs of each?
2. What type(s) of translation(s), if any, affect the range of a logarithmic function?
3. What type(s) of translation(s), if any, affect the domain of a logarithmic function?
4. Consider the general logarithmic function . Why can’t x be zero?
5. Does the graph of a general logarithmic function have a horizontal asymptote? Explain.
For the following exercises, state the domain and range of the function.
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For the following exercises, state the domain and the vertical asymptote of the function.
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For the following exercises, state the domain, vertical asymptote, and end behavior of the function.
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For the following exercises, state the domain, range, and x- and y-intercepts, if they exist. If they do not exist, write DNE.
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For the following exercises, match each function in the graph below with the letter corresponding to its graph.
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For the following exercises, match each function in the figure below with the letter corresponding to its graph.
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For the following exercises, sketch the graphs of each pair of functions on the same axis.
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36. and
37. and
For the following exercises, match each function in the graph below with the letter corresponding to its graph.
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For the following exercises, sketch the graph of the indicated function.
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For the following exercises, write a logarithmic equation corresponding to the graph shown.
47. Use as the parent function.
48. Use as the parent function.
49. Use as the parent function.
50. Use as the parent function.
For the following exercises, use a graphing calculator to find approximate solutions to each equation.
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56. Let b be any positive real number such that . What must be equal to? Verify the result.
57. Explore and discuss the graphs of and . Make a conjecture based on the result.
58. Prove the conjecture made in the previous exercise.
59. What is the domain of the function ? Discuss the result.
60. Use properties of exponents to find the x-intercepts of the function algebraically. Show the steps for solving, and then verify the result by graphing the function.
Candela Citations
- Precalculus. Authored by: Jay Abramson, et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution. License Terms: Download for free at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface