# How do you find the range of y = ln(x+3)?

Apr 12, 2015

The graph of this function is identical to hte $y = \ln x$ but only translated of three units to the left.

So the domain is $\left(- 3 , + \infty\right)$, and the range is $\left(- \infty , + \infty\right)$.

The graph is:

graph{ln(x+3) [-10, 10, -5, 5]}

Apr 12, 2015

Range (0, inf)

To find the range of this function, consider the exponential form ${e}^{y}$ = x+3 of this function. It is quite obvious that no real y exists for this function if x+3 $\le$0. Hence x+3 has to be any positive real number only. This can occur for all positive or negative values y. It can therefore be concluded that range of the function is all real numbers(R).