Question

What is the equation of the vertical asymptote of

f(x)=2log5(x+1)−3 ?

Enter your answer in the box. x =

Answer 1

x=-1

Explanation:

The given equation is
`f(x)=2 log5(x+1)-3`

vertical asymptote is by finding the values that make the equation undefined so the above equation is satisfied when x= -1

There is no horizontal asymptote

The equation of the vertical assymptote of

`f(x)=2 log5(x+1)-3`

⇒
`f(x)=2 log(5x+5)-3`

⇒
`y= log((5x+1)^2)-3`

Answer 2

x=-1

Explanation:

Consider parent function
`y=\log_5x.` The graph of this function has vertical asymptote
`x=0.`

The graph of the function
`f(x)=\log_5(x+1)-3` can be obtained from the graph of the parent function by translation 1 unit to the left and 3 units down. This means that vertical asymptote is also transleted 1 unit to the left and 3 units down. Translating the vertical line
`x=0` 1 unit to the left and 3 units down you will get the line
`x=-1.`