Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 43

Chapter 3, Problem 43

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

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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