Stitz-Zeager_College_Algebra_e-book

Turning our attention to y intercepts we set x 0 and

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Unformatted text preview: is means (−x, y ) satisﬁes the equation and hence is on the graph. In this way, we can check whether the graph of a given equation possesses any of the symmetries discussed in Section 1.1. The results are summarized below. Steps 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. Intercepts and symmetry are two tools which can help us sketch the graph of an equation analytically, as evidenced in the next example. Example 1.3.3. Find the x- and y -intercepts...
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