Answer:
At x = 13, the expression inside the absolute value bars becomes 0, so F(13) = |0| + 11 = 11. Therefore, the vertex of the graph of F(x) is the point (13, 11).
Explanation:
The graph of the function F(x) = |x - 13| + 11 is the graph of the absolute value function shifted 13 units to the right and 11 units up from the origin. The vertex of this graph is the point where the absolute value function changes direction, which is at the point (13, 11).
To see why this is the case, consider the definition of the absolute value function:
|x| = x, if x >= 0
|x| = -x, if x < 0
The function F(x) = |x - 13| + 11 is a translation of the absolute value function by 13 units to the right and 11 units up. This means that the vertex of the graph will occur at the point where the absolute value function changes direction, which is at x = 13.
At x = 13, the expression inside the absolute value bars becomes 0, so F(13) = |0| + 11 = 11. Therefore, the vertex of the graph of F(x) is the point (13, 11).