Question

question 22 of 25
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:

The function \( F(x) = \ln x + 2 \) is a vertical shift of the parent function \( \ln x \) (shifted up by 2 units). Key properties: domain is \( x > 0 \) (only right of y-axis), increasing (since derivative \( \frac{1}{x} > 0 \) for \( x > 0 \)), and at \( x=1 \), \( F(1) = 0 + 2 = 2 \) (so it passes through (1,2)). Graph B has domain \( x > 0 \), is increasing, and passes through a point near (1,2) (consistent with the shift). Graphs A (too low at x=1), C (goes to negative y at small x, unlike \( \ln x +2 \)), D (decreasing) do not match.

Answer:

B. Graph B