Question

which of these could be the graph of ( f(x)=ln x + 2 )?
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Recall the parent function

The parent function of \(F(x)=\ln x + 2\) is \(y = \ln x\). The domain of \(y=\ln x\) is \(x>0\), and it has a vertical asymptote at \(x = 0\). The function \(y=\ln x\) passes through the point \((1,0)\) since \(\ln(1)=0\).

Step2: Analyze the transformation

For the function \(F(x)=\ln x+2\), it is a vertical shift of the parent function \(y = \ln x\) by \(2\) units up.
When \(x = 1\), \(F(1)=\ln(1)+2=0 + 2=2\).

Answer:

C. Graph C