IM Alg2.2.9 Lesson: End Behavior (Part 2)
Match each of the graphs to the polynomial equation it represents.
For the graph without a matching equation, write down what must be true about the polynomial equation.
Write an equation for a polynomial with the following properties:
it has even degree, it has at least 2 terms, and, as the inputs get larger and larger in either the negative or positive directions, the outputs get larger and larger in the negative direction. Pause here so your teacher can review your work.
Write an equation for a polynomial with the following properties:
it has odd degree, it has at least 2 terms, as the inputs get larger and larger in the negative direction the outputs get larger and larger in the positive direction, and as the inputs get larger and larger in the positive direction, the outputs get larger and larger in the negative direction.
In the given graph all of the horizontal intercepts are shown.
Find a function with this general shape and the same horizontal intercepts.
and are each functions of defined by and . Describe the end behavior of and .
For >, which function do you think has greater values? Be prepared to share your reasoning with the class.