How To Graph An Absolute Value Function: Symmetric And V-Shaped Graph Tutorial

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The graph of an absolute value function is a V-shaped graph. It is symmetric around the origin, which means that the left and right sides of the graph are mirror images of each other.

The equation of an absolute value function is typically written in the form f(x) = |x|. This means that the output (y-value) of the function is the absolute value of the input (x-value).

To graph an absolute value function, we start by plotting a few points. We can choose some easy values of x, like -2, -1, 0, 1, and 2. Then we plug each of those values into the equation f(x) = |x| to see what y-value we get. For example, if we plug in x = -2, we get f(-2) = |-2| = 2. So the point (-2, 2) is on the graph.

Once we have a few points, we can sketch the V-shaped graph. The lowest point of the V is at the origin (0, 0). The arms of the V extend upwards and outwards at a 45-degree angle.

It is important to note that the absolute value function is not differentiable at x = 0. This means that the slope of the graph changes abruptly at that point. The slope on the left side of the graph is negative and the slope on the right side is positive.

Overall, the graph of an absolute value function is a simple but important graph that comes up frequently in mathematics and science.

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