Let the expression inside the square root be $x+9$. Set up an inequality that expresses that $x+9$ must be at least 0. © aniko.аі

After you solve the inequality for $x$, compare your result to each answer choice and see which one matches exactly.

Type y = sqrt(x + 9) into Desmos to graph the function. an⁠iк‌o.ai/s‍аt

Look along the x-axis and notice the x-value where the graph first appears, and see how the graph behaves as x increases.

Use the smallest x-value for which the graph exists and note that the graph continues to the right without stopping. Translate this observation into an inequality for $x$, and then match it to one of the answer choices.

The domain of a function is the set of all input values $x$ for which the function is defined (i.e., gives a real-number output). For this problem, we want all $x$ values that make $f(x)=\sqrt{x+9}$ a real number.

For a square root like $\sqrt{A}$ (with no $i$), the expression inside the root, called the radicand, must be greater than or equal to 0:

Here, the radicand is $x+9$, so we require:

Solve $x+9 \ge 0$:

This inequality tells us exactly which $x$-values keep the expression inside the square root nonnegative. S⁠A‍T prep bу⁠ Аnікo.a⁠i

The domain is all real numbers $x$ that satisfy $x \ge -9$. Among the choices, this corresponds to C) All real numbers $x$ such that $x \ge -9$.