What are the features of the function f(x)=−2log3 (x+4) graphed below?

The function f(x) is a logarithmic function with a vertical asymptote of x = -4. The range of the function is (-∞, ∞), and it is decreasing on its domain of (-4, ∞). The end behavior on the LEFT side is as x → -4 (from the right), y → ∞, and the end behavior on the RIGHT side is as x → ∞, y → -∞.

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xero099 xero099 · Answer 2 · 2022-03-01T13:06:12+01:00

The characteristics of the logarithmic function are described below:

Domain of the function is [tex](-4, +\infty)[/tex]
Range of the function is the set of all real numbers.
The component [tex]x+4[/tex] indicates the existence of a vertical asymptote at [tex]x=-4[/tex].
The constant [tex]-2[/tex] reflects the logarithm about the x-axis.

Analysis of a logarithmic function

The graph of the function is attached below. After a quick analysis, we conclude the following characteristics of the given function:

Domain of the function is [tex](-4, +\infty)[/tex]
Range of the function is the set of all real numbers.
The component [tex]x+4[/tex] indicates the existence of a vertical asymptote at [tex]x=-4[/tex].
The constant [tex]-2[/tex] reflects the logarithm about the x-axis.

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