Understanding Absolute Value Functions and Graphing
The absolute value function is a fundamental concept in mathematics that creates V-shaped graphs. The absolute value parent function is written as y = |x|, which forms a V-shape centered at the origin. When graphing absolute value functions, understanding transformations is crucial for accurate visualization.
To graph an absolute value function, start by identifying the vertex point h,k. The vertex represents the turning point of the V-shape, where h indicates horizontal shift and k shows vertical shift. For example, in y = |x - 2| + 3, the vertex is at (2,3). The graph maintains symmetry around a vertical line through the vertex.
Definition The absolute value function returns the positive distance of a number from zero on a number line, creating a V-shaped graph when plotted.
When working with coefficients in front of x, such as y = 2|x|, the graph becomes steeper (stretched vertically) if the coefficient is greater than 1, and wider (compressed) if the coefficient is less than 1. This understanding is essential for graphing absolute value functions with a number in front of x.
The domain of absolute value function includes all real numbers, while the range starts from the vertex's y-coordinate and extends upward. Students can verify their work using a graphing calculator or Desmos graphing tool, which provides immediate visual feedback.