Specific Expectations

By the end of this course, students will…

1.1  recognize a polynomial expression (i.e., a series of terms where each term is the product of a constant and a power of x with a non- negative integral exponent); recognize the equation of a polynomial function, give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions

1.2  compare, through investigation using graphing technology, the numeric, graphical, and algebraic representations of polynomial (i.e., linear, quadratic, cubic, quartic) functions (e.g., compare finite differences in tables of values; investigate the effect of the degree of a polynomial function on the shape of its graph and the maximum number of x-intercepts; investigate the effect of varying the sign of the leading coefficient on the end behaviour of the function for very large positive or negative x-values)

1.3  describe key features of the graphs of polynomial functions (e.g., the domain and range, the shape of the graphs, the end behaviour of the functions for very large positive or negative x-values)

Learning Goals

By the end of the lesson, students will…

• Distinguish between polynomial and non-polynomial functions and be able describe the characteristics of polynomial functions
• Understand the effect that the sign of the leading coefficient have on a polynomial function and its end behaviours
• Distinguish between odd-degree and even-degree power functions

Success Criteria

• I can list the characteristics of odd and even degree functions
• I can determine the end behaviours, number of turning points, and the number of x-intercepts for a given polynomial function