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Concept

Absolute Value Function

An absolute value function is a function that contains an absolute value expression.

y = ∣ x - 1 ∣ + 1

An absolute value graph has a distinct $V -$ shape. It is symmetric about the vertical line that passes through its vertex. The vertex of an absolute value function is the point where the graph changes direction.

Graph of the absolute value function y=|x-1|+1 which opens upwards and has a vertex at (1,1).

Since the graph of $y = ∣ x - 1 ∣ + 1$ changes direction at $(1, 1),$ this point is the vertex. Additionally, the graph is symmetric about the line $x = 1 .$

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