y=|x|
The equation y = |x| represents an absolute value function
The equation y = |x| represents an absolute value function. In this case, the function takes any value of x, applies the absolute value function to it, and assigns the result to y.
The absolute value function, denoted by |x|, returns the positive value or magnitude of the number x. It essentially gives you the distance of x from the origin (0) on the number line, regardless of the sign.
To graph this absolute value function, you can start by identifying a few key points:
1. When x is positive or zero (x ≥ 0), the absolute value function is equal to x itself. So, for x ≥ 0, we have y = x.
2. When x is negative (x < 0), the absolute value function becomes positive. So, for x < 0, we have y = -x, which is the negative value of x. Using these observations, you can plot a few points on the graph: When x = 0, y = 0. When x = 1, y = 1. When x = -1, y = 1. By connecting these points, you get a V-shaped graph. The point (0, 0) is the vertex or the lowest point of the V, and the arms of the V extend to positive and negative infinity. The graph of y = |x| looks like a straight line with a corner at the origin (0, 0) and always stays above or on the x-axis. It reflects any negative values of x to their positive counterparts because the absolute value of any negative number is positive.
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