Logarithmic Functions: f(x)=alog_(b)(x-h)+k f(x)=log_(b)x,b > 1 Domain: Range: Vertical Asymptote:

Identify Base Impact: Identify the base of the logarithm and its impact on the function. Since b > 1, the base is a valid positive number not equal to 1, which is necessary for the logarithmic function to be defined.Find Domain: Find the domain of f(x) = log_b(x). The logarithmic function is defined only for x > 0. Therefore, the domain of f(x) = log_b(x) is all positive real numbers.Determine Range: Determine the range of f(x) = log_b(x). The output of a logarithmic function can be any real number, which means the range of f(x) is all real numbers.Identify Vertical Asymptote: Identify the vertical asymptote of f(x) = log_b(x). The vertical asymptote occurs where the function is undefined and near which the function heads towards negative or positive infinity. For log_b(x), this is at x = 0.

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Q. Logarithmic Functions:

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f(x)=a\log_{b}(x-h)+k

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f(x)=\log_{b}x

b > 1

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Domain:

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Range:

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Vertical Asymptote:

Identify Base Impact: Identify the base of the logarithm and its impact on the function. $\newline$ Since b > 1, the base is a valid positive number not equal to $1$ , which is necessary for the logarithmic function to be defined.
Find Domain: Find the domain of $f(x) = \log_b(x)$ . The logarithmic function is defined only for x > 0. Therefore, the domain of $f(x) = \log_b(x)$ is all positive real numbers.
Determine Range: Determine the range of $f(x) = \log_b(x)$ . The output of a logarithmic function can be any real number, which means the range of $f(x)$ is all real numbers.
Identify Vertical Asymptote: Identify the vertical asymptote of $f(x) = \log_b(x)$ . The vertical asymptote occurs where the function is undefined and near which the function heads towards negative or positive infinity. For $\log_b(x)$ , this is at $x = 0$ .