Question

graph the following function, and identify the domain and range. list any intercepts or asymptotes. describe the end behavior.
$y = \log_2 x$
a. $\\{x|x < 0\\}$
b. $\\{x|x > 0\\}$
c. $\\{x|-10 < x < 10\\}$
d. the domain is the set of all real numbers.
what is the range of the function?
a. $\\{y|y < 0\\}$
b. $\\{y|y > 0\\}$
c. $\\{y|-10 < y < 10\\}$
d. the range is the set of all real numbers.

Explanation:

Step1: Recall the domain of logarithmic functions

For the function \(y = \log_{a}x\) (\(a>0,a
eq1\)), the argument \(x\) must be positive. So for \(y=\log_{2}x\), \(x>0\).

Step2: Recall the range of logarithmic functions

The logarithmic function \(y = \log_{a}x\) (\(a>0,a
eq1\)) can take any real - valued output. As \(x\to0^{+}\), \(y=\log_{2}x\to-\infty\) and as \(x\to+\infty\), \(y = \log_{2}x\to+\infty\).

Answer:

• Domain: B. \(\{x|x > 0\}\)
• Range: D. The range is the set of all real numbers.