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Describing Graphs of Polynomial Functions

Describing Graphs of Polynomial Functions 1.13 - Solution

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Before we begin, let's recall two important definitions.

  • A function has even symmetry when for all in its domain.
  • A function has odd symmetry when for all in its domain.
Let's see how the graphs of these types of functions look.
Even functions

Odd functions

Reset

Consider the graphs above. We can see that for even symmetry, if is on the graph, then is also on the graph. Meanwhile, for an odd symmetry, if is on the graph, then is also on the graph. Now, consider the given function. Let's calculate
Next, let's calculate
Finally, let's think about what these results tell us.

Since and the function is neither an even nor an odd function.