Graph the function below. Determine the domain, range, and vertical asymptote. Please show all of your work. Graph the function below. Determine the... |

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` .