Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
8. Analyzing Graphs of Polynomial Functions
Continue to next subchapter

Exercise 7 Page 215

A function is an even function when for all in its domain. A function is an odd function when for all in its domain.

Odd

Practice makes perfect

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

  • A function is an even function when for all in its domain.
  • A function is an odd function when for all in its domain.
Let's see how the graphs of these types of functions look.
Consider the graphs above. We can see that for even functions, if is on the graph, then is also on the graph. Meanwhile, for an odd function, if is on the graph, then is also on the graph. Now, consider the given function.
Let's calculate
Simplify right-hand side
Next, let's calculate
Finally, let's think about what these results tell us.

We can see above that Therefore, is an odd function.