Symmetry Properties of Graphs: Reflection Symmetry with Respect to Axes and Origin - Prof., Study notes of Algebra

Download Symmetry Properties of Graphs: Reflection Symmetry with Respect to Axes and Origin - Prof. and more Study notes Algebra in PDF only on Docsity! SYMMETRY – objective 7c A graph is said to be symmetric with respect to the x-axis, if for every point (x,y) on the graph, the point (x,-y) is also on the graph. So if (1,2) is on the graph, then so is (1,-2). To test for symmetry: Replace y by –y in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the x-axis. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * A graph is said to be symmetric with respect to the y-axis, if for every point (x,y) on the graph, the point (-x,y) is also on the graph. So if (5,3) is on the graph, then so is (-5,3). To test for symmetry: Replace x by –x in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the y-axis. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * A graph is said to be symmetric with respect to the origin, if for every point (x,y) on the graph, the point (-x,-y) is also on the graph. So if (2,4) is on the graph, then so is (-2,-4). To test for symmetry: Replace x by –x and y by –y in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the origin.