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

Key Concepts

Absolute Value Function

The absolute value function, denoted as y = |x - a|, represents the distance of x from a on the number line. It produces a V-shaped graph that opens upwards, with the vertex located at the point (a, 0). Understanding this function is crucial for analyzing its symmetry and behavior.

Symmetry in Graphs

Symmetry in graphs refers to the property where a graph is identical on either side of a specific line, known as the line of symmetry. For functions like y = |x - a|, the line of symmetry is vertical and can be found at x = a, indicating that the function behaves the same for values equidistant from this line.

Vertical Line Equation

A vertical line in the Cartesian plane is represented by an equation of the form x = k, where k is a constant. This line runs parallel to the y-axis and indicates that for any value of y, x remains constant. Identifying the correct value of k is essential for determining the line of symmetry for the given absolute value function.