Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. |y| = -x

Key Concepts

Symmetry in Graphs

Symmetry in graphs refers to the property where a graph remains unchanged under certain transformations. For example, a graph is symmetric with respect to the x-axis if replacing y with -y yields the same equation. Similarly, it is symmetric with respect to the y-axis if replacing x with -x results in the same equation, and it is symmetric with respect to the origin if replacing both x and y with their negatives preserves the equation.

Absolute Value Functions

Absolute value functions, denoted as |y|, represent the distance of y from zero on the number line, which is always non-negative. This means that |y| = -x implies that y can only take on values that are zero or positive, as the left side cannot be negative. Understanding how absolute values behave is crucial for analyzing the symmetry of the graph.

Graphing Techniques

Graphing techniques involve plotting points and understanding the shape and behavior of equations on a coordinate plane. To determine symmetry, one can graph the equation or analyze it algebraically by substituting values for x and y. This helps visualize how the graph behaves in relation to the axes and the origin, which is essential for identifying the type of symmetry present.