Explanation To test whether the graph of y = 2 x 2 − 3 is symmetry with respect to the x -axis, replace y with − y in y = 2 x 2 − 3 , − y = 2 x 2 − 3 The above equation is not equivalent to the original equation y = 2 x 2 − 3 . Therefore, the graph of the equation y = 2 x 2 − 3 is not symmetric with respect to the x -axis. To test the graph of y = 2 x 2 − 3 is symmetry with respect to the y -axis, replace x with − x in y = 2 x 2 − 3 , y = 2 ( − x ) 2 − 3 y = 2 x 2 − 3 The above equation is equivalent to the original equation y = 2 x 2 − 3 . Therefore, the graph of the equation y = 2 x 2 − 3 is symmetric with respect to the y -axis

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Chapter 4.1, Problem 39E

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To test: Whether the graph of the equation y=2x2−3 is symmetric with respect to the x-axis, the y-axis and/or the origin and confirm it graphically.

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Chapter 4.1, Problem 38E

Chapter 4.1, Problem 40E

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To test: Whether the graph of the equation y = 2 x 2 − 3 is symmetric with respect to the x -axis, the y -axis and/or the origin and confirm it graphically.

Solution Summary: The author explains that the graph of the equation y=2x 2-3 is not symmetric with respect to the x -axis.

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To test: Whether the graph of the equation y=2x2−3 is symmetric with respect to the x-axis, the y-axis and/or the origin and confirm it graphically.

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Chapter 4 Solutions