Math Example: Absolute Value Functions: Example 15

Topic

Special Functions

Description

The image shows a graph of the absolute value function y = |3x - 1| + 4. The graph opens upwards and is narrower than y = |x|, with the vertex marked at (1/3, 4). This example demonstrates how a coefficient greater than 1, a constant inside the absolute value, and a constant outside the absolute value affect the graph's steepness, horizontal position, and vertical position. Absolute value functions are a fundamental concept in algebra, introducing students to equations that involve taking the absolute value of a variable or expression. This example illustrates how multiple changes in the equation impact the resulting graph's shape, steepness, and position. Providing multiple worked-out examples is essential for students to fully grasp the concept of absolute value functions. By examining different scenarios, students can identify patterns and develop a deeper understanding of how these functions behave. This approach helps reinforce important concepts such as the characteristic V-shape of absolute value graphs, the impact of coefficients greater than 1 on the graph's steepness, how constants inside the absolute value affect the horizontal position, and how constants outside the absolute value influence the vertical position. Through repeated exposure to diverse examples, students can build intuition and improve their ability to analyze and graph absolute value functions independently.

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