Understanding the Graph of the Absolute Value Parent Function | A Foundation for Graphing Complex Functions

Graph of Absolute Value Parent Function

The graph of the absolute value parent function, denoted by f(x) = |x|, is a V-shaped graph that passes through the origin (0,0)

The graph of the absolute value parent function, denoted by f(x) = |x|, is a V-shaped graph that passes through the origin (0,0). It consists of two linear segments that intersect at the origin and form a 90-degree angle.

To understand the graph better, let’s examine the behavior of the function for different values of x:

1. For positive values of x: When x is positive, the absolute value of x is equal to x itself. So, f(x) = |x| = x. In this case, the graph is a straight line with a positive slope, starting from the origin and extending upwards to the right. It represents how the function increases linearly as x gets larger.

2. For negative values of x: When x is negative, the absolute value of x is equal to the opposite of x. So, f(x) = |x| = -x. In this case, the graph is also a straight line with a positive slope, but this time it starts from the origin and extends upwards to the left. It represents how the function increases linearly as x becomes more negative.

By combining these two linear segments, we obtain the complete graph of the absolute value parent function. It is symmetric with respect to the y-axis since the absolute value of a negative value is the same as the absolute value of its positive counterpart. This symmetry is evident in the V-shape of the graph.

The graph of the absolute value parent function is a fundamental building block for understanding and graphing more complex functions involving absolute values.

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