Understanding the Absolute Value Function | Graph, Symmetry, and Key Points

Absolute Value Function (Graph)

The absolute value function is a mathematical function that computes the distance of a number from zero on the number line

The absolute value function is a mathematical function that computes the distance of a number from zero on the number line. It is denoted by the symbol “|x|”.

The graph of the absolute value function is a V-shaped curve, also known as a “V-curve” or a “V-shape”. The vertex of the V-curve is located at the point (0, 0), which represents the absolute value of zero (|0| = 0). The arms of the V-curve extend upwards and downwards from the vertex.

The key characteristic of the absolute value function’s graph is its symmetry. The graph is symmetric with respect to the vertical axis, which means that if you reflect any point on one side of the axis onto the opposite side, you would get an equivalent point. This symmetry is due to the nature of absolute value, where the distance from zero is always positive, regardless of the sign of the number.

When graphing the absolute value function, it is helpful to identify certain key points. For example, the point (1, 1) corresponds to |1| = 1, and the point (-1, 1) corresponds to |-1| = 1. Similarly, points (2, 2) and (-2, 2) represent the absolute value of 2 and -2, respectively.

As you move away from the vertex, the values of x and y increase or decrease at the same rate. This means that as x increases, y also increases, and as x decreases, y decreases. The arms of the V-curve never touch or cross the x-axis because the absolute value of any number is always positive or zero.

Overall, the graph of the absolute value function provides a visual representation of how the distance of a number from zero relates to its value. It helps us understand the concept of absolute value and can be used to solve various mathematical problems and equations.

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