Question

what is the domain of the function $y = \log(x + 3)$?
$\bigcirc$ $(-\infty,\infty)$ $(-\infty, \infty)$
$\bigcirc$ $(-\infty, -3)$
$\bigcirc$ $(0, \infty)$
$\bigcirc$ $(-3, \infty)$

Explanation:

Step1: Recall log domain rule

For \( y = \log(u) \), \( u > 0 \).

Step2: Apply to given function

Here, \( u = x + 3 \), so \( x + 3 > 0 \).

Step3: Solve inequality

Subtract 3: \( x > -3 \).

Answer:

\((-3, \infty)\) (the last option, e.g., if options are labeled as D. \((-3, \infty)\), then D. \((-3, \infty)\))