L1.2 A2 Polynomial Functions - Part 4
Completion requirements
Unit 1
Functions
Read
Page 108 of your Pre-Calculus 12 textbook refers to the end behaviour of a graph.
Considering the end behaviour of a graph is a good way to help picture a function’s graph.
Determining what the left endpoint of a graph is doing, or where it is extending, and then doing the same for the right endpoint of a graph will help you visualize the graph of a function.
Two things to consider when thinking about a graph’s end behaviour are the degree of the polynomial and the sign of the leading coefficient.
As seen in the above chart in this lesson and the chart on page 109 in your Pre-Calculus 12 textbook, the degree of a function determines the general shape of the function’s graph.
The sign of the leading coefficient will help you determine the end behaviour of the function.
Then, by determining specific points, such as the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math»-intercepts and the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-intercepts, more details about the shape of the graph are revealed.
For more details and examples, see section 3.1, pages 106 to 113 in your Pre-Calculus 12 textbook.
Determining what the left endpoint of a graph is doing, or where it is extending, and then doing the same for the right endpoint of a graph will help you visualize the graph of a function.
Two things to consider when thinking about a graph’s end behaviour are the degree of the polynomial and the sign of the leading coefficient.
As seen in the above chart in this lesson and the chart on page 109 in your Pre-Calculus 12 textbook, the degree of a function determines the general shape of the function’s graph.
The sign of the leading coefficient will help you determine the end behaviour of the function.
Then, by determining specific points, such as the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math»-intercepts and the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-intercepts, more details about the shape of the graph are revealed.
For more details and examples, see section 3.1, pages 106 to 113 in your Pre-Calculus 12 textbook.