Math Example: Absolute Value Functions: Example 21

Topic

Special Functions

Description

The image shows a graph of the absolute value function y = |-3x - 5| - 2. The graph is plotted on a coordinate plane, with the vertex marked as a red dot at (-1 2/3, -2). The graph opens upwards and is narrower than y = |x|. This example illustrates how a negative coefficient, a constant inside the absolute value, and subtracting a constant outside affect the graph's steepness, horizontal position, and vertical position. Absolute value functions are a crucial concept in algebra, introducing students to equations that involve taking the absolute value of a variable or expression. This example demonstrates 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 comprehend 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 negative coefficients 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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