Question

select all the correct answers. which statements are true about the graph of function f? ( f(x)=log x ) 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. the graph has a domain of ( {x |-infty<x<infty} ) and approaches 0 as ( x ) decreases. the graph has a range of ( {y | 0<y<infty} ) and decreases as ( x ) approaches 0.

Explanation:

Step1: Analyze the domain of \(y = \log x\)

The function \(y=\log x\) is defined for \(x>0\). So the domain is \(\{x|0 < x<\infty\}\). As \(x\to0^{+}\), \(\log x\to-\infty\), not \(0\). So the first option is wrong.

Step2: Analyze the range of \(y = \log x\)

The range of the logarithmic function \(y = \log x\) is \(\{y|-\infty

Step3: Re - check the first option's domain and behavior

The domain of \(y = \log x\) is not \(\{x|-\infty < x<\infty\}\), so the third option is wrong.

Step4: Re - check the range of the function

The range of \(y=\log x\) is not \(\{y|0 < y<\infty\}\), so the fourth option is wrong.

Answer:

The second option: The graph has a range of \(\{y|-\infty < y < \infty\}\) and decreases as \(x\) approaches \(0\)