S ECTION 1.2.1 Graphs of Equations. T HE F UNDAMENTAL G RAPHING P RINCIPLE The graph of an equation is the set of points which satisfy the equation. That.

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Presentation transcript:

S ECTION Graphs of Equations

T HE F UNDAMENTAL G RAPHING P RINCIPLE The graph of an equation is the set of points which satisfy the equation. That is, a point (x,y) is on the graph of an equation if and only if x and y satisfy the equation

E XAMPLES Determine if (2,-1) is on the graph of x 2 + y 3 = 1 Graph x 2 + y 3 = 1 ->

I NTERCEPTS A point at which a graph meets the x-axis is called an x-intercept of the graph. A point at which a graph meets the y-axis is called an y-intercept of the graph.

S TEPS FOR FINDING THE INTERCEPTS OF THE GRAPH OF AN EQUATION Given an equation involving x and y: The x-intercepts always have the form (x,0) To find the x-intercepts of the graph, set y = 0 and solve for x The y-intercepts always have the form (0,y) To find the y-intercepts of the graph, set x = 0 and solve for y

S TEPS FOR TESTING IF THE GRAPH OF AN EQUATION POSSESSES SYMMETRY To test the graph of an equation for symmetry About the y-axis: Substitute (-x,y) into the equation and simplify If the result is equivalent to the original equation, the graph is symmetric about the y-axis About the x-axis: Substitute (x,-y) into the equation and simplify. If the result is equivalent to the original equation, the graph is symmetric about the x-axis. About the origin: Substitute (-x,-y) into the equation and simplify If the result is equivalent to the original equation, the graph is symmetric about the origin.

E XAMPLE Find the x- and y-intercepts (if any) of the graph of (x - 2) 2 + y 2 = 1 Test for symmetry Plot additional points as needed to complete the graph