Find the domain and intercepts. \( f(x)=\sqrt{x+36} \) Find the domain Select the correct choi A. The domain of the function \( f(x) \) is Bype your answer in interval no B. The domain is all real numbers.

To find the domain of the function \( f(x) = \sqrt{x + 36} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative, since the square root of a negative number is not defined in the real number system. ### Step 1: Set the expression under the square root greater than or equal to zero. \[ x + 36 \geq 0 \] ### Step 2: Solve the inequality. Subtract 36 from both sides: \[ x \geq -36 \] ### Step 3: Write the domain in interval notation. The domain of \( f(x) \) is all values of \( x \) that are greater than or equal to -36. In interval notation, this is expressed as: \[ [-36, \infty) \] ### Step 4: Find the intercepts. #### x-intercept: To find the x-intercept, set \( f(x) = 0 \): \[ \sqrt{x + 36} = 0 \] Squaring both sides gives: \[ x + 36 = 0 \] Solving for \( x \): \[ x = -36 \] So, the x-intercept is at the point \((-36, 0)\). #### y-intercept: To find the y-intercept, evaluate \( f(0) \): \[ f(0) = \sqrt{0 + 36} = \sqrt{36} = 6 \] So, the y-intercept is at the point \((0, 6)\). ### Summary: - The domain of the function \( f(x) \) is \([-36, \infty)\). - The x-intercept is at \((-36, 0)\). - The y-intercept is at \((0, 6)\). ### Final Answer: A. The domain of the function \( f(x) \) is \([-36, \infty)\).