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The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions.
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- Graphing Absolute Value Functions
We can graph any absolute value equation of the form...
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This topic covers: Solving absolute value equations. Graphing absolute value functions. Solving absolute value inequalities.
21 wrz 2023 · To solve an absolute value equation, such as \(|X| = p\), replace it with the two equations \(X = −p\) and \(X = p\) and then solve each as usual. Absolute value equations can have up to two solutions.
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 the absolute value function f (x) = |x|. It is important to note that the equation of the left-hand branch of the “V” is y = −x. Typical points on this branch are (−1, 1), (−2, 2), (−3, 3), etc. It is equally important to note that the right-hand branch of the “V” has equation y = x.
Graphing an Absolute Value Function. The most significant feature of the absolute value graph is the corner point at which the graph changes direction. This point is shown at the origin in Figure 2. Figure 2. Figure 3 shows the graph of y = 2|x– 3| + 4. y = 2 | x – 3 | + 4.
Write an absolute value function whose parent graph has been compressed horizontally by a factor of \( \frac{3}{2} \), translated five units right, and translated two units down.
