Graphing Absolute Value Functions

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What is an absolute value function?

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An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, resulting in a non-negative output.

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What is the general form of an absolute value function?

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How does the value of 'a' affect the graph of an absolute value function?

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If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the steeper the graph.

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The vertex is the point (h, k) on the graph, which is the highest or lowest point depending on the value of 'a'.

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The vertex is found at the point (-2, 5). Here, h = -2 and k = 5.

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The graph is a V-shape that opens upwards with the vertex at the origin (0, 0).

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Adding a constant outside the absolute value shifts the graph vertically. In this case, the graph shifts up by 3 units.

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Subtracting a constant outside the absolute value shifts the graph vertically down. In this case, the graph shifts down by 2 units.

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How do you determine the y-intercept of an absolute value function?

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To find the y-intercept, set x = 0 in the function and solve for y.

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