Questions and Answers
Which is the graph of a logarithmic function?
Which is the graph of f(x) = log3x?
Which function is shown in the graph?
What is the domain of the function?
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What is the range of the function?
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What is the inverse of the logarithmic function f(x) = log9x?
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How can you use a point on the graph of f-1(x) = 9^x to determine a point on the graph of f(x) = log9x?
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Which points lie on the graph of f(x) = log9x? Check all that apply.
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What is the sound intensity of rustling leaves in decibels?
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The sound intensity of a whisper is how many times the reference intensity?
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Which best describes the graph of f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x?
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Given that the point (8, 3) lies on the graph of g(x) = log2x, which point lies on the graph of f(x) = log2(x + 3) + 2?
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What is the domain of f(x) = log2(x + 3) + 2?
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Which graphs represent a logarithmic function f?
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What are the domain and range of the logarithmic function f(x) = log7x?
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Study Notes
Graphing Logarithmic Functions
- The correct graph of a logarithmic function is identified as option C.
- The graph representing f(x) = log3x corresponds to option B.
- The function depicted by a specific graph is f(x) = log5x.
Domain and Range
- For logarithmic functions, the domain is x > 0, indicating the input must be positive.
- The range of logarithmic functions includes all real numbers, allowing for any output value.
Inverse Functions
- The inverse of the logarithmic function f(x) = log9x is F-1(x) = 9^x.
- To find a point on the graph of f(x) = log9x using its inverse, switch the x and y coordinates of the known point.
Points on Graph
- Points belonging to the graph of f(x) = log9x include C, E, and F.
- A whisper, equivalent to 30 decibels, represents a sound intensity that is 1000 times the reference intensity.
Sound Intensity
- The sound intensity of rustling leaves, being 100 times the reference intensity, translates to 20 decibels.
Transformations of Graphs
- The transformation of g(x) = log2x to f(x) = log2(x + 3) + 2 involves a translation of 3 units left and 2 units up.
- Given the point (8, 3) on g(x), the corresponding point on f(x) = log2(x + 3) + 2 is (5, 5).
Domain of Transformed Functions
- The domain of f(x) = log2(x + 3) + 2 is defined as x > -3, indicating valid inputs.
Domain and Range with Inverses
- For f(x) = log7x, the domain aligns with the range of its inverse function, while the range matches the domain of the inverse function.
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Test your understanding of logarithmic function graphs with these flashcards. This quiz covers various aspects, including graphical representation and properties of logarithmic functions, relevant to your assignments. Perfect for students looking to reinforce their knowledge of this topic.
