Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.