Question

How do you graph `k(x) = ln (x + 3) + 6`?

Answer 1

Use the parent function `y = ln(x)` and shift it horizontally `3` to the left (`-3`) and vertically up `6`

Explanation:

The parent function `y = ln(x)` goes through `(1, 0)`:

graph{ln x [-7.04, 12.96, -5.36, 4.64]}

Shift it horizontally `3` to the left `ln(x+3)` so it goes through `(-2, 0)` which is an `x` shift of `-3` from `(1, 0)` :
graph{ln (x+3) [-7.04, 12.96, -5.36, 4.64]}

Shift it vertically up `6`, `ln(x+3) + 6` so `(-2, 0)` moves up to `(-2, 6)`:
graph{ln(x+3) +6 [-4.58, 15.42, -0.64, 9.36]}