Graphing Absolute Value Functions: Step-by-Step Guide and Characteristics

Graph of Absolute Value

The graph of an absolute value function is a commonly studied topic in mathematics

The graph of an absolute value function is a commonly studied topic in mathematics. The absolute value function is defined as:

| x | =
x if x is greater than or equal to 0,
-x if x is less than 0.

The graph of the absolute value function y = | x | appears as a V-shaped graph with the vertex at the origin (0, 0). The two arms of the graph extend upwards and downwards along the y-axis from the vertex.

To graph the absolute value function, you can follow these steps:

Step 1: Identify the vertex.
Since the vertex of the absolute value function is at the origin (0, 0), mark this point on the coordinate plane.

Step 2: Plot additional points.
To plot additional points, substitute different x-values into the absolute value function and determine the corresponding y-values.

For example:
– If x = -3, then y = | -3 | = 3. Plot the point (-3, 3).
– If x = -2, then y = | -2 | = 2. Plot the point (-2, 2).
– If x = -1, then y = | -1 | = 1. Plot the point (-1, 1).
– If x = 0, then y = | 0 | = 0. This is the vertex, so no additional point is plotted.
– If x = 1, then y = | 1 | = 1. Plot the point (1, 1).
– If x = 2, then y = | 2 | = 2. Plot the point (2, 2).
– If x = 3, then y = | 3 | = 3. Plot the point (3, 3).

Step 3: Join the plotted points.
Use a straight line segment to connect the plotted points, including the vertex. Draw a V-shaped graph that extends upwards and downwards along the y-axis.

The resulting graph should resemble a “V” shape, with the vertex at the origin (0, 0) and the arms extending upwards and downwards along the y-axis.

Note that the graph of the absolute value function is symmetric with respect to the y-axis, meaning that if you reflect one arm of the graph across the y-axis, you will obtain the other arm.

Remember, when dealing with more complex absolute value functions, such as those involving additional terms or coefficients, the shape of the graph may be stretched or compressed. However, the V-shaped characteristic of the absolute value function will still be evident.

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