Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
2. Graphing Rational Functions
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Exercise 49 Page 371

Note that the graph of an even function has even symmetry, which means that it is symmetric about the y-axis. On the other hand, the graph of an odd function has odd symmetry, which means that it is symmetric about the origin.

Graph:

Even, odd, or neither? Odd

Practice makes perfect
We will graph the following rational function using a graphing calculator. Then, we will determine whether the function is even, odd, or neither. y=x^3/3x^2+x^4 To draw a graph on a calculator, we first press the Y= button and type the function in one of the rows. Having written the function, we can push GRAPH to draw it.

Now, let's consider the characteristics of the graphs of an even function and odd function.

  • Even Function: The graph of an even function has even symmetry, which means that it is symmetric about the y-axis.
  • Odd Function: The graph of an odd function has odd symmetry, which means that it is symmetric about the origin.

Therefore, because the graph of the given function is symmetric about the origin, it is an odd function.