Sullivan Algebra and Trigonometry: Section 2.2 Graphs of Equations Objectives Graph Equations by Plotting Points Find Intercepts from a Graph Find Intercepts from an Equation Test an Equation for Symmetry with Respect to the x- axis, y-axis, and the origin

The graph of an equation in two variables x and y consists of the set of points in the xy-plane whose coordinates (x,y) satisfy the equation. Example: Is (3,5) on the graph of ? Substitute x = 3 and y = 5 into the equation: True! Therefore, (3,5) is on the graph of the equation.

Graph yx  35 Example :

By plotting the points found in the previous step, the graph can be drawn:

The points, if any, at which the graph crosses or touches the coordinate axes are called the intercepts. Procedure for Finding Intercepts 1. To find the x-intercept(s), if any, of the graph of an equation, let y = 0 in the equation and solve for x. 2. To find the y-intercept(s), if any, of the graph of an equation, let x = 0 in the equation and solve for y.

Example: Find the x-intercepts and y-intercepts (if any) of the graph of To find the x-intercepts (if any), let y = 0. Therefore, the x-intercepts are (7,0) and (-2,0) To find the y-intercepts (if any), let x = 0. Therefore, the y-intercept is (0,-14)

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. If a graph is symmetric with respect to the x-axis and the point (3, 5) is on the graph, then (3, -5) is also on the graph.

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. If a graph is symmetric with respect to the y-axis and the point (3, 5) is on the graph then (-3, 5) is also on the graph.

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. If a graph is symmetric with respect to the origin and the point (3, 5) is on the graph then (-3, -5) is also on the graph.

Example: Test for symmetry. x-axis: Replace y with -y: Since replacing y with -y produces a different equation, the equation is not symmetric about the x-axis. y-axis: Replace x with -x: Since replacing x with -x produces the same equation, the equation is symmetric about the y-axis.

origin: Replace y with -y and x with -x. Example: Test for symmetry. Since replacing y with -y and x with -x produces a different equation, the equation is not symmetric about the origin.