Question

graph the following function, and identify the domain and range. list any intercepts or asymptotes. describe the end behavior

$y = \log_{0.5}x$

what is the domain of the function?

$\bigcirc$ a. $\\{ x | x > 0 \\}$

$\bigcirc$ b. $\\{ x | - 10 < x < 10 \\}$

$\bigcirc$ c. $\\{ x | x < 0 \\}$

$\bigcirc$ d. the domain is the set of all real numbers.

Explanation:

Step1: Recall the domain of logarithmic functions

For a logarithmic function \(y = \log_{a}x\) (\(a>0,a
eq1\)), the argument \(x\) must be positive. In the function \(y=\log_{0.5}x\), the argument is \(x\).

Step2: Determine the domain

Since \(x>0\) for the function \(y = \log_{0.5}x\) (because the logarithm of a non - positive number is not defined in the set of real numbers).

Answer:

A. \(\{x|x > 0\}\)