Graphing Logarithmic Functions Assignments

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.