Find the domain and intercepts. \[ f(x)=\sqrt{x+36} \] Find the domain. Select the corroct choice below and, if necessary, fill in the answer box to completo yout choice. A. The domain of the function \( f(x) \) is \( \{-36, \infty\rangle \). (Type your answer in interval notation.) B. The domain is all real numbers. Find the \( x \)-intercept(s). Select the correct choce below and, if necessary, fill in the answer box to complele your choice. A. The \( x \)-intercept(s) of the graph is (are) \( x= \) \( \square \) \( \square \). (Simplity your answor. Type an integer or a decimal. Use a comma to separato answers as needed.) B. There is no \( x \)-intercept

**Step 1. Find the Domain** For the function \[ f(x)=\sqrt{x+36}, \] the expression inside the square root must be nonnegative. This gives the inequality: \[ x+36 \ge 0. \] Subtract 36 from both sides: \[ x \ge -36. \] Thus, the domain of the function is: \[ [-36, \infty). \] **Step 2. Find the \(x\)-intercept(s)** The \(x\)-intercepts occur where \(f(x)=0\). Set the function equal to 0: \[ \sqrt{x+36} = 0. \] Square both sides (or observe directly), which implies: \[ x+36 = 0. \] Subtract 36 from both sides: \[ x = -36. \] Thus, the \(x\)-intercept is at: \[ (-36,0). \] **Answers:** - **Domain:** Choice A. The domain of the function \( f(x) \) is \([ -36, \infty )\). - **\(x\)-intercept(s):** Choice A. The \(x\)-intercept of the graph is \( x=-36 \).