select the correct answer. which statements are true about the graph of function f? f(x)=ln x a. the graph…

select the correct answer. which statements are true about the graph of function f? f(x)=ln x a. the graph has a domain of {x|-∞ < x < ∞} and an x - intercept of (1,0). b. the graph has a range of {x|0 < x < ∞} and a y - intercept of (0,1). c. the graph has a domain of {x|0 < x < ∞} and an x - intercept of (1,0). d. the graph has a range of {x|-∞ < x < ∞} and a y - intercept of (0,1).

select the correct answer. which statements are true about the graph of function f? f(x)=ln x a. the graph has a domain of {x|-∞ < x < ∞} and an x - intercept of (1,0). b. the graph has a range of {x|0 < x < ∞} and a y - intercept of (0,1). c. the graph has a domain of {x|0 < x < ∞} and an x - intercept of (1,0). d. the graph has a range of {x|-∞ < x < ∞} and a y - intercept of (0,1).

Answer

Explanation:

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

The function (y=\ln x) is defined when (x>0). So the domain is ({x|0 < x<\infty}).

Step2: Analyze the (x -)intercept

Set (y = 0), then (\ln x=0). Since (\ln x = 0) when (x = e^{0}=1), the (x -)intercept is ((1,0)).

Step3: Analyze the range

The range of (y = \ln x) is ({y|-\infty<y<\infty}). Also, for the (y -)intercept, when (x = 0), (\ln x) is undefined.

Answer:

C. The graph has a domain of ({x|0 < x < \infty}) and an (x -)intercept of ((1,0))