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

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.

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.

Answer

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<y<\infty}). As (x) approaches (0) from the right ((x\to0^{+})), (y=\log x) decreases (since (\log x_1-\log x_2=\log\frac{x_1}{x_2}), if (0 < x_1<x_2), then (\frac{x_1}{x_2}<1) and (\log\frac{x_1}{x_2}<0)).

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)