What is the vertical asymptote for the function f (x) = ln (x + 4) - 2? Be sure to write your answer as an equation for a line.

F (x) = ln (x+4) - 2

Change f (x) to y

y=ln (x+4) - 2

Inverse x and y

x=ln (y+4) - 2

Solve for y, result will be inverse.

x+2=ln (y+4)

convert to exponential form

e^ (x+2) = y+4

y=e^ (x+2) - 4

This is the inverse.

f^-1 (x) = e^ (x+2) - 4

Looking at the above function, it is (e^x) shifted to the left by two unit, being brought down (4) units. The only important part of this function is the down-shift of (4), because this represents the horizontal asymptote.

y = - 4 is the horizontal asymptote, which means

for f (x) = ln (x+4) - 2

x=-4 is a vertical asymptotes.