Final answer:
The vertex of the absolute value function y = |x - 5| + 4 is (5, 4), and the range of this function is 4 ≤ y < ∞. The correct option is B) (5, 4); 4 ≤ y < ∞.
Step-by-step explanation:
The function given is y = |x - 5| + 4. The function represents an absolute value equation which is V-shaped and opens upwards. The vertex of this function is the point where the expression inside the absolute value becomes zero. Therefore, when x - 5 = 0, the vertex is at x = 5. Adding the constant 4 gives us the y-coordinate of the vertex which is y = 4. So, the vertex of the function is (5, 4).
The range of this function is the set of all possible values of y. Since the absolute value expression opens upwards, and there is an addition of 4, the smallest value y can take is 4. The function increases without bound as x moves away from 5, either to the left or the right. Therefore, the range is 4 ≤ y < ∞ or in interval notation [4, ∞).
Hence, the correct option is B) (5, 4); 4 ≤ y < ∞.