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Chapter 3.2

Q. 3.2.7

Finding the Domain of a Logarithmic Function

Find the domain of f(x)=\log _4(x+3).

Step-by-Step

Verified Solution

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.

3.13