y = |x|
The equation y = |x| represents the absolute value function
The equation y = |x| represents the absolute value function. The absolute value function takes any real number x and returns its non-negative value. In other words, it gives the distance between the number x and zero on the number line.
To understand this, let’s break down the equation:
1. When x is positive or zero (x ≥ 0): We simply take the value of x itself since it is already non-negative. For example, if x = 3, y = |3| = 3. If x = 0, y = |0| = 0.
2. When x is negative (x < 0): We take the negative value of x and turn it into a positive value. For example, if x = -3, y = |-3| = 3. If x = -5, y = |-5| = 5. In essence, the graph of y = |x| is a V-shaped graph that opens upwards. It passes through the origin (0,0) because the absolute value of 0 is 0. For positive values of x, the graph increases linearly. For negative values of x, the graph decreases linearly with the same rate as the positive side. To illustrate this, you can plot some points: x |x| ------------- -3 3 -2 2 -1 1 0 0 1 1 2 2 3 3 Joining these points will give you a V-shaped graph centered at the origin and opening upwards. I hope this explanation helps! Let me know if there are any additional questions or if you need further clarification.
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