1. Lesson 1

1.6. Explore 2

Mathematics 30-2 Module 4

Module 4: Polynomials

 

textbook

Read “Explore the Math” on pages 274 and 275 of your textbook. In particular, pay attention to the definition for end behaviour. You should also read the definition for turning point on page 275. You will use end behaviour and turning points to help describe the characteristics of polynomial graphs.



Try This 2

 

Open Polynomial Function Explorer.

 

 

 

This is a play button for Polynomial Function Explorer.

 

Your goal is to determine the following:

  • number of possible x-intercepts
  • number of possible y-intercepts
  • end behaviour
  • domain
  • range
  • number of possible turning points

Drag the blue points to explore the shapes of each type of function. (Click the buttons to change the function type.) It may be helpful to choose “Show x-intercepts” and “Show y-intercept.”

 

A table like the one that follows will help you organize your results.

 

Type of Function

Constant

Linear

Quadratic

Cubic

Degree

0

1

2

3

Example Function

f(x) = a

f(x) = ax + b

f(x) = ax2 + bx + c

f(x) = ax3 + bx2 + cx + d

Possible Number of
x-intercepts

 

 

 

 

Possible Number of
y-intercepts

 

 

 

 

End Behaviour

 

 

 

 

Domain

 

 

 

 

Range

 

 

 

 

Number of Possible Turning Points

 

 

 

 

Adapted from PRINCIPLES OF MATHEMATICS 12 by Canavan-McGrath et al. Copyright Nelson Education Ltd. Reprinted with permission.

 

course folder Save your responses in your course folder.