Odd and Even Functions

Odd and Even Functions

Dr. Rowlett

Open Ended

This video will summaries today's objectives: identifying odd and even functions, and determining their end behaviors.

Can you look at a graph of a polynomial to determine whether it is odd or even? Explain?

Fill in the Blanks

If the leading coefficient is

, then the polynomial is increasing overall.

Fill in the Blanks

If the highest exponent is odd, then the function is

.

Multiple Select

Draw a polynomial such that...

• It is even

• It is negative

• Has a zero at x=-2 and x=4

• Has a y-intercept at (0,3).

Open Ended

Draw a polynomial that is odd, negative, with only one zero at x = 6. Describe its end behavior.

Multiple Choice

All quadratics (parabolas) are

• Even

• Odd

Multiple Choice

Parabolas that are concave down have a _____ value.

• Maximum

• Minimum

Multiple Choice

A quadratic that is negative has a ______.

• Maximum

• Minimum

Multiple Choice

A quadratic that has a minimum value is ....

• positive

• negative

Open Ended

Watch this brief overview of even and odd functions.

True or False: All parabolas are even.

Open Ended

Go to www.desmos.com and graph

 $y=2x^3-x$  . Is this function odd or even? Explain while discussing the leading coefficient, the highest power, and its graph.

Open Ended

Graphs and polynomial equations tell a powerful story!

True or False: All quadratics are positive?

Open Ended

Now, go to www.desmos.com and graph

 $y=-2x^3-x$ .  Describe the tails? Is this graph negative or positive? Is the function odd or even? 

Open Ended

Watch this video on the end behavior of graph's of polynomials.

If the tails are pointing in the same direction, is the polynomial odd or even?