select all the correct answers. which statements are true about the graph of function f? f(x)=log x the…

Explanation:

Step1: Recall domain of logarithmic function

The domain of $y = \log x$ is the set of positive real - numbers. Mathematically, the domain is ${x|0 < x<\infty}$. So, the statement "The graph has a domain of ${x|0 < x < \infty}$ and approaches 0 as x decreases" is considered for domain analysis. The statement "The graph has a domain of ${x|-\infty < x < \infty}$ and approaches 0 as x decreases" is incorrect because the logarithm of non - positive numbers is undefined in the set of real numbers.

Step2: Recall range of logarithmic function

The range of the function $y=\log x$ is the set of all real numbers, i.e., ${y|-\infty < y < \infty}$. As $x$ approaches 0 from the right ($x\rightarrow0^{+}$), $y = \log x\rightarrow-\infty$, which means the function decreases as $x$ approaches 0. The statement "The graph has a range of ${y|0 < y < \infty}$ and decreases as x approaches 0" is incorrect because the range of the common logarithm function is not restricted to positive real numbers only. The statement "The graph has a range of ${y|-\infty < y < \infty}$ and decreases as x approaches 0" is correct.

Answer:

The graph has a domain of ${x|0 < x < \infty}$ and approaches 0 as x decreases; The graph has a range of ${y|-\infty < y < \infty}$ and decreases as x approaches 0.