In which direction does the absolute value function graph always open?

The absolute value function graph always opens upwards in a V-shape due to the nature of how absolute value is defined. The absolute value of a number is the distance from zero, regardless of whether the number itself is positive or negative. This means that when you plot an absolute value function, such as ( y = |x| ), as the input values increase in either the positive or negative direction, the output values (y-values) never go below zero. Instead, they rise to create a V-shape with a vertex at the origin (0,0).

As you move away from the vertex along the x-axis in both directions, the values of y increase, resulting in the characteristic upward opening. This behavior is consistent across all transformations of the absolute value function as well, since any vertical shifts will maintain the upward opening feature of the graph.