Questions: Graph the function with a graphing calculator. Then, visually estimate the domain and the range. f(x) = sqrt(19-x) Graph the function f(x) = sqrt(19-x) with a graphing calculator. Choose the correct graph below. A. [-30,30,-10,10] B. [-30,30,-10,10] C. [-10,40,-10,10] D. [-40,10,-10,10]

Solution Steps

The function \(f(x) = \sqrt{19 - x}\) is a square root function. The value inside the square root must be non-negative.

The domain of the function is the set of all possible x-values for which the function is defined. Since the expression inside the square root must be greater than or equal to zero, we have \(19 - x \ge 0\). This simplifies to \(x \le 19\). So, the domain is \((-\infty, 19]\).

Since the square root function always returns a non-negative value, the smallest value of \(f(x)\) is 0, which occurs when \(x = 19\). As x decreases, \(19 - x\) increases, and so does \(\sqrt{19 - x}\). Therefore, the range is \([0, \infty)\).

The graph should start at \(x = 19\) and extend to the left. Option B is the correct graph because it depicts a square root function that starts at \(x = 19\) and decreases as x decreases. Options C and D depict increasing functions, and option A is an increasing square root function that starts at the origin. Option B matches the expected graph with the domain ending at \(x = 19\). The given window of [-30, 30, -10, 10] is not the best viewing window, but the general shape of the graph is correct.

Final Answer