Finding the Domain of a Logarithmic Function
Find the domain of f(x)=\log _4(x+3).
The domain of f consists of all x for which x + 3 > 0. Solving this inequality for x, we obtain x > -3. Thus, the domain of f is (-3, ∞). This is illustrated in Figure 3.13. The vertical asymptote is x = -3 and all points on the graph of f have x-coordinates that are greater than -3.