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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.

Sagot :

Pulkit
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. 
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