Section 1.2 graphs of equations in two variables;intercepts; symmetry
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This document discusses graphs of equations in two variables and their properties. It examines intercepts, symmetry, and determining whether points lie on graphs. The document contains examples of finding the x-intercepts and y-intercepts of graphs, identifying symmetric graphs, and testing equations for symmetry with respect to the x-axis, y-axis, and origin. It also determines whether given points satisfy equations and identifies other points that must be on a graph based on its symmetry.
Section 1.2 graphs of equations in two variables;intercepts; symmetry
- 1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry
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- 4. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine if the following points are on the graph of the equation − 3x +y = 6 (b) (−2, 0)(a) (0, 4) (c) (−1, 3) −4 −3 −2 −1 1 2 −2 −1 1 2 3 4 ( )0 43 4 6− + = ≠ ( )3 62 0− − + = ( )3 3 61 33− + = + =−
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- 12. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the x-intercept(s) and the y-intercept(s) of the graph of then graph by plotting points. 2 4y x= −
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- 15. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a graph is symmetric with respect to the x-axis and the point (3,2) is on the graph, what other point is also on the graph? −4 −3 −2 −1 1 2 3 4 5 −4 −3 −2 −1 1 2 3 4 (3,2) (3,−2)
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- 17. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a graph is symmetric with respect to the y-axis and the point (3,2) is on the graph, what other point is also on the graph? −4 −3 −2 −1 1 2 3 4 5 −4 −3 −2 −1 1 2 3 4 (− 3, 2) (3,2)
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- 19. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a graph is symmetric with respect to the origin and the point (3,2) is on the graph, what other point is also on the graph? −4 −3 −2 −1 1 2 3 4 5 −4 −3 −2 −1 1 2 3 4 (− 3, − 2) (3,2)
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- 22. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 2 2 9 Test for symmetry. 2 x y x − = + x-Axis: 2 2 9 2 x y x − − = + Not equivalent so not symmetric with respect to the x-axis. y-Axis: ( ) ( ) 2 2 9 2 x y x − − = − + IS equivalent so symmetric with respect to the y-axis. Origin: ( ) ( ) 2 2 9 2 x y x − − − = − + Not equivalent so not symmetric with respect to the origin.
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