The graph of y=|x-2| is symmetric with respect to a vertical line. What is the equation of that line?

검증된 단계별 안내

Recall that the graph of an absolute value function of the form \(y = |x - h|\) is symmetric about the vertical line \(x = h\).

Identify the value of \(h\) in the given function \(y = |x - 2|\). Here, \(h = 2\).

Understand that the symmetry line is the vertical line passing through \(x = h\), which means the line is \(x = 2\).

This vertical line acts as the axis of symmetry for the graph, meaning the graph is a mirror image on either side of this line.

Therefore, the equation of the line of symmetry for the graph \(y = |x - 2|\) is \(x = 2\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Absolute Value Function

An absolute value function outputs the distance of a number from zero, always producing non-negative values. The graph of y = |x - h| forms a 'V' shape with its vertex at (h, 0), reflecting the point where the expression inside the absolute value equals zero.

Symmetry in Graphs

Symmetry in graphs means the graph looks the same on both sides of a line or point. For absolute value functions, the graph is symmetric about a vertical line passing through the vertex, which acts as the axis of symmetry.

Axis of Symmetry for Absolute Value Functions

The axis of symmetry for y = |x - h| is the vertical line x = h. This line divides the graph into two mirror-image halves, indicating that the function's value depends only on the distance from h, not the direction.