Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 17: 50

Answer

Plot $(0, -2)$ and $(5, -3)$, then connect them including $(-4, 0)$ using a smooth curve. Refer to the graph below.

Work Step by Step

In order to obtain the complete graph, we have to plot the points, symmetric to the given points already plotted on the graph. For symmetry with respect to the $x$-axis, if the point $(x,y)$ is on the graph, then the point $(x,-y)$ is also on the graph. Thus, Since $(0,2)$ is on the graph, then $(0,-2)$ should also be on the graph. Since $(5,3)$ is on the graph, then $(5,-3)$ should also be on the graph. Plot the points then connect them including $(-4, 0)$ using a smooth curve to complete the graph. Refer to the graph above.
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