Graphing the Absolute Value Function: Step-by-Step Guide with Examples

Absolute Value Function Graph

The absolute value function is a piecewise function that can be defined as follows:

– For x ≥ 0, f(x) = x
– For x < 0, f(x) = -x The graph of the absolute value function is a V-shaped graph that opens upwards

The absolute value function is a piecewise function that can be defined as follows:

– For x ≥ 0, f(x) = x
– For x < 0, f(x) = -x The graph of the absolute value function is a V-shaped graph that opens upwards. The vertex of the graph is the origin (0, 0) and the graph is symmetric with respect to the y-axis. To graph the absolute value function, you can follow these steps: 1. Identify the vertex: The vertex of the absolute value function is always at the origin (0, 0). 2. Plot some points: To get a better idea of the shape of the graph, you can plot a few points. Start with x = -2, -1, 0, 1, 2 and substitute these values into the function to find the corresponding y-values. For example, when x = -2, f(x) = |-2| = 2. Therefore, the point (-2, 2) is on the graph. Similarly, when x = 2, f(x) = |2| = 2. So the point (2, 2) is also on the graph. Plot these points on the graph. 3. Draw the graph: Connect the plotted points with a V-shaped line that opens upwards. Make sure to extend the graph indefinitely in both directions. It is important to note that the slope of the lines on either side of the vertex is 1, indicating that the absolute value function increases by 1 unit for every 1 unit increase in x. Additionally, any negative value of x will be reflected across the y-axis to create a positive y-value, while any positive value of x will have the same y-value. I hope this helps! Let me know if you have any further questions.

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