Question

question 3 of 6 (1 point) | question attempt: 1 of 2
below is the graph of $y = \ln x$.
translate it to become the graph of $y = \ln(x + 3) + 2$.

Explanation:

Step1: Identify horizontal shift

For $y=\ln(x+3)$, shift left 3 units.
Original key point $(1,0)$ becomes $(1-3,0)=(-2,0)$.

Step2: Identify vertical shift

For $y=\ln(x+3)+2$, shift up 2 units.
The point $(-2,0)$ becomes $(-2,0+2)=(-2,2)$.

Step3: Translate entire graph

Apply the same shifts to all points on $y=\ln x$: every point $(x,y)$ on $y=\ln x$ moves to $(x-3,y+2)$.

Answer:

The graph of $y=\ln(x+3)+2$ is the original $y=\ln x$ graph shifted 3 units to the left and 2 units upward. Key reference point: the original $(1,0)$ moves to $(-2,2)$, and the vertical asymptote $x=0$ shifts to $x=-3$.