Absolute value parent function
f(x)=|x|Domain: {x| -∞ < x < ∞}Range: {y| ∞ < y < ∞}x & y intercept: (0,0)Max # of roots/zeros: 2Continuous
The absolute value parent function is a type of function in algebra that takes the absolute value of an input variable x and returns a positive output value. It can be denoted by the equation y = |x|, where the vertical bars indicate the absolute value of x.
The absolute value function is a V-shaped graph that is symmetric about the y-axis. The lowest point on the graph (the vertex) is at the origin (0,0), and it increases steeply as x moves away from zero in either direction. This means that as x increases, y also increases, but the slope changes abruptly at x = 0.
The absolute value parent function is often used as a starting point for creating transformations of the function. By applying different types of operators to manipulate the function, it is possible to shift, stretch, compress, or reflect the graph of the absolute value function to create different shapes and patterns.
One common application of absolute value functions is in modeling situations where quantities can only take on positive values (such as the distance between two points) or the magnitude of a quantity is more important than its direction (such as temperature, where negative values are not physically meaningful).
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