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 $x>0$, or in interval - notation $(0,\infty)$. So the domain is ${x|0 < x<\infty}$. As $x$ approaches $0$ from the right, $\log x\to-\infty$, not $0$. So the first statement about the domain is correct and the second one is wrong.

Step2: Recall range of logarithmic function

The range of the logarithmic function $y = \log x$ is all real numbers, i.e., ${y|-\infty < y<\infty}$. As $x$ approaches $0$ from the right, the function $y = \log x$ decreases (since the logarithmic - function $y=\log x$ is an increasing function for $x > 0$, and as $x$ gets closer to $0$, the value of $y$ gets more and more negative). So the third statement about the range is correct and the fourth one is wrong.

Answer:

The graph has a domain of ${x|0 < x<\infty}$ and approaches $0$ as $x$ decreases. (False) The graph has a domain of ${x|-\infty < x<\infty}$ and approaches $0$ as $x$ decreases. (False) The graph has a range of ${y|-\infty < y<\infty}$ and decreases as $x$ approaches $0$. (True) The graph has a range of ${y|0 < y<\infty}$ and decreases as $x$ approaches $0$. (False) So the correct answer is: The graph has a range of ${y|-\infty < y<\infty}$ and decreases as $x$ approaches $0$.