i know the domain is (-3 , infinity)
y = ln(x+3)
i thought it was [-4, infinity) but i checked on a calculator and it goes passed -4. And i cannot use a calculator
The range of a function is the set of numbers the function can achieve. The natural log has a range $\displaystyle (-\infty,\infty)$. However, its domain is $\displaystyle (-3,\infty)$. The domain is the set of numbers for which the function is defined. Natural log can take numbers from $\displaystyle (0,\infty)$. So we just need to check when $\displaystyle x+3 > 0$.