Understanding the Absolute Value Function: Graphing Tips and Key Points

graph of absolute value

To graph the absolute value function, we need to understand what it represents

To graph the absolute value function, we need to understand what it represents. The absolute value function gives us the distance between a number and zero on a number line.

The general form of the absolute value function is:

f(x) = |x|

To graph f(x) = |x|, we will focus on the key points, the x-intercepts, and the slope changes.

1. Key points:
– When x = 0, f(x) = |0| = 0. So, the point (0,0) is on the graph.
– When x > 0, f(x) = x. So, for any positive value of x, f(x) will also be positive and equal to x.
– When x < 0, f(x) = -x. So, for any negative value of x, f(x) will be positive and equal to -x. 2. X-intercepts: - The x-intercepts occur when f(x) = 0. Since the absolute value of any number is always positive, the absolute value function has no x-intercepts. 3. Slope changes: - The absolute value function changes its slope at x = 0. On the left side of the y-axis, the slope is negative, and on the right side, the slope is positive. - The slope of the graph becomes steeper as we move away from the y-axis. Now, let's create a graph by plotting some points: Point A: (2, 2) Point B: (1, 1) Point C: (0, 0) Point D: (-1, 1) Point E: (-2, 2) Using these points, we can start plotting the graph. The resulting graph should look like a "V" shape, with the vertex at (0,0), opening upwards. | 3 | * | * | * |* -2 -1 O 1 2 |* | * | * -3 | * The graph of the absolute value function follows the pattern of a "V" shape, symmetric about the y-axis, with the vertex at (0,0). The slope of the graph changes from negative on the left side of the vertex to positive on the right side. I hope this helps you understand how to graph the absolute value function. Let me know if you have any further questions.

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