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

Verified step by step guidance

1. Step 1: Understand the concept of symmetry. A graph is symmetric with respect to a vertical line if, when you fold the graph along that line, the left and right halves of the graph coincide.
2. Step 2: Identify the function. The function given is y=|x-2|. This is an absolute value function, which is always symmetric with respect to a vertical line.
3. Step 3: Identify the line of symmetry. For an absolute value function y=|x-h|, the line of symmetry is always x=h.
4. Step 4: Apply the concept to the given function. In the function y=|x-2|, the line of symmetry is x=2.
5. Step 5: Write down the equation of the line of symmetry. The equation of the line of symmetry for the function y=|x-2| is x=2.

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.