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Chapter 3: Problem 107

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of a function with origin symmetry can rise to the left and rise to the right.

Short Answer

Expert verified
The statement 'The graph of a function with origin symmetry can rise to the left and rise to the right' is false. The correct statement should be: 'The graph of a function with origin symmetry can rise to the left and fall to the right, or fall to the left and rise to the right.'.

Step by step solution

01

Step 1- Evaluate the statement

Consider the given statement: 'The graph of a function with origin symmetry can rise to the left and rise to the right'. Here the discussion is around the behaviour of the graph of an origin symmetric function.
02

Step 2- Understanding Origin Symmetry

Remember that a function has origin symmetry if its graph is unchanged when rotated 180 degrees about the origin. If a part of the graph is rising to the left of the origin, the graph should be falling to the right of the origin in order to maintain this symmetry and vice-versa.
03

Step 3- Validation of the statement

Based on the understanding of origin symmetry, it is not possible for the graph of an origin symmetric function to rise on both sides of the origin. Hence the given statement is false.

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