Absolute Value Functions

The absolute value of a number is its distance from zero on the number line, always expressed as a positive value.

Absolute value is talking about distance, and distance is always measured by positive numbers.

The vertex is (3, 4).

The transformation is represented by the function y = |x - 4|.

The vertex represents the minimum or maximum point of the graph, depending on its orientation.

The general form is f(x) = a|bx - h| + k, where (h, k) is the vertex.

This function shifts the graph of y = |x| up by 5 units.

This function shifts the graph of y = |x| right by 2 units and down by 3 units.

The coefficient 'a' affects the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

The vertex is (0, 0).