y=|x|
absolute value parent function
The equation y=|x| represents a graph of a v-shaped function that passes through the origin (0,0) and is symmetric about the y-axis.
When x is positive, the absolute value of x is equal to x itself. So, the graph of y=|x| will be identical to y=x in the positive x-axis.
When x is negative, the absolute value of x is equal to the opposite of x, which is positive. So, the graph of y=|x| will be identical to y=-x in the negative x-axis.
Therefore, the overall shape of the graph is a v-shaped curve. The curve begins at the origin, turns around at x=0 and continues to increase as you move towards the positive side of the x-axis and also continues to increase as you move towards the negative side of the x-axis.
Additionally, the slope of the graph changes at x=0. At x=0, the slope of the graph changes from negative to positive, making it a point of inflection for the function.
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