You need to remember that the domain of function consists of all values of x that make the equation of the function possible, hence you need to remember that logarithmic function`ln(x+5)` exists if `x+5gt0` .
You need to solve the inequality `x+5gt0` to find the domain of the function.
`x+5gt0 =gt xgt-5 =gt x in (-5,oo)`
You should remember that the range of logarithmic function corresponds to the domain of exponential function, hence the range of the function is R.
You need to solve the equation x + 5 = 0 to find the vertical asymptote of the function, such that:
`x + 5 = 0 =gt x = -5`
The graph of the function is sketched below such that:
Hence, the domain of the function `f(x) = ln(x+5)` is interval `(-5,oo), ` the range is the set R and the vertical asymptote is `x = -5` .