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General form of an absolute value equation: f ( x) = a | x − h | + k. The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h and k tell us how far the graph shifts horizontally and vertically. Some examples: Graph of y=|x|. Graph of y=3|x|. Graph of y=-|x|. Graph of y=|x+3|-2.
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- Graphing Absolute Value Functions
We can graph any absolute value equation of the form...
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5 maj 2020 · Learn how to graph absolute value functions in this video math tutorial by Mario's Math Tutoring. We discuss how to graph the parent function as well as the transformations of the form...
We can graph any absolute value equation of the form y=k|x-a|+h by thinking about function transformations (horizontal shifts, vertical shifts, reflections, and scalings).
The graph of y=|x-h|+k is the graph of y=|x| shifted h units to the right and k units up. See worked examples practicing this relationship.
An absolute value function is an important function in algebra that consists of the variable in the absolute value bars. The general form of the absolute value function is f (x) = a |x - h| + k, where (h, k) is the vertex of the function.
Given an absolute value function, solve for the set of inputs where the output is positive (or negative). Set the function equal to zero, and solve for the boundary points of the solution set. Use test points or a graph to determine where the function’s output is positive or negative.
Here are 2 examples illustrating the procedure for finding the function rule. Example. Find the function rule for the absolute value function with vertex at (2, 1) through (5, 13). Solution. Since the vertex is at (2, 1), we know that h = 2 and k = 1 Therefore f ( x) = a | x 2 | + 1 is the equation of the function.
