Understanding the Absolute Value Function: Explained and Illustrated

y = |x|

The equation y = |x| represents the absolute value function

The equation y = |x| represents the absolute value function. The absolute value of a number is its distance from zero on the number line, so this function takes any input value x and returns its absolute value as the output value y.

To understand this function, let’s break it down for different values of x:

1. For x > 0:
When x is a positive number, |x| is equal to x itself. So, y = x.
For example, if x = 3, then y = |3| = 3. Similarly, if x = 7, then y = |7| = 7.

2. For x = 0:
When x is zero, |x| is also zero. So, y = 0.
For x = 0, y = |0| = 0.

3. For x < 0: When x is a negative number, |x| is equal to the opposite of x. So, y = -x. For example, if x = -4, then y = |-4| = 4. Similarly, if x = -2, then y = |-2| = 2. The graph of y = |x| is a V-shaped graph, known as the "absolute value graph." It opens upwards and has its vertex at the origin (0, 0). The graph is symmetric with respect to the y-axis. In summary, the equation y = |x| represents the absolute value function, where the output (y) is the non-negative distance of the input (x) from zero on the number line.

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