Question

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).

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

Answer:

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