Question

How are the coordinates of the vertex related to the axis of symmetry and the range of an absolute value function?

A) The x-coordinate of the vertex represents the axis of symmetry, while the y-coordinate represents the minimum or maximum value of the absolute value function.
B) The y-coordinate of the vertex represents the axis of symmetry, while the x-coordinate represents the minimum or maximum value of the absolute value function.
C) The equation of the absolute value function determines the coordinates of the vertex, which in turn determine the axis of symmetry and the range.

Answer 1

The x-coordinate of the vertex corresponds to the axis of symmetry of an absolute value function, and the y-coordinate defines the minimum or maximum value, determining the function's range.

Step-by-step explanation:

The coordinates of the vertex of an absolute value function are directly related to the axis of symmetry and the range of the function. The correct relationship is: A) The x-coordinate of the vertex represents the axis of symmetry, while the y-coordinate represents the minimum or maximum value of the absolute value function. The axis of symmetry is a vertical line that passes through the vertex, splitting the graph into two mirror images. The vertex, therefore, represents the point where the function changes direction, which is either its highest or lowest point, depending on whether the absolute value function opens upwards or downwards.