Graph the function below. Determine the domain, range, and vertical asymptote. Please show all of your work.
Graph the function below. Determine the domain, range, and vertical asymptote. Please show all of your work. f(x)=ln(x+5)
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` .