Absolute Value Parent Function Graph
The absolute value parent function is a mathematical function denoted as “f(x) = |x|”, where the absolute value of x is the distance between x and 0 on the number line
The absolute value parent function is a mathematical function denoted as “f(x) = |x|”, where the absolute value of x is the distance between x and 0 on the number line. The absolute value function takes any real number input and returns its non-negative value.
To graph the absolute value function, we can start by plotting the points for various x-values, and then connecting those points with a V-shaped graph. Here are the steps to graph the absolute value parent function:
1. Plot the points for positive x-values:
– Choose two positive x-values, for example, x = 1 and x = 2.
– Determine the corresponding y-values by evaluating |x| at those x-values. For instance, f(1) = |1| = 1 and f(2) = |2| = 2.
– Plot the points (1, 1) and (2, 2) on the coordinate plane.
2. Plot the points for negative x-values:
– Choose two negative x-values, for example, x = -1 and x = -2.
– Determine the corresponding y-values by evaluating |x| at those x-values. For instance, f(-1) = |-1| = 1 and f(-2) = |-2| = 2.
– Plot the points (-1, 1) and (-2, 2) on the coordinate plane.
3. Connect the plotted points:
– Draw a V-shaped line connecting the points on the coordinate plane. The vertex of the V should intersect with the y-axis at (0, 0).
– The graph will continue indefinitely in both the positive and negative directions.
The resulting graph of the absolute value parent function resembles a “V” shape, with the vertex at the origin. It is symmetric with respect to the y-axis, meaning that for every point (x, y) on the graph, the point (-x, y) is also on the graph.
The absolute value parent function graph is commonly used as a reference point for transforming and graphing other absolute value functions by applying translations, reflections, stretches, or compressions.
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