Overview
| Site: | Farwell |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Overview |
| Printed by: | Guest user |
| Date: | Sunday, November 24, 2024, 5:00 AM |
Description
Overview
In this unit, students will expand upon their knowledge of polynomial equations and functions. Students will learn to identify and perform mathematical operations on polynomial functions, factor and solve polynomial equations both algebraically and graphically. It is anticipated that this unit will take from four to five weeks in a traditional hourly schedule.
Students Will Be Able To
After successful completion of this unit, students will be able to:
- Recognize the number of zeros of a polynomial function and the relationship to the linear components (factors) of the polynomial function.
- Describe the end behavior for a polynomial function, determine if a function is even or odd, and identify any symmetry related to the function.
- Describe the effects of the leading coefficient (stretching and shrinking), and the effects of the degree of a polynomial function.
- Identify relative maximums and minimums for a polynomial function.
- Solve polynomials graphically.
- Identify the domain and range of a polynomial function in the context of a situation.
- Determine if a given situation can be modeled by a polynomial function or not. If it is a polynomial function, write a function to model it. Include linear and quadratic functions.
Mastered HSCEs
The following Michigan High School Content Expectations will be mastered in this unit:
A3.5.1 Write the symbolic form and sketch the graph of simple polynomial functions.
A3.5.2 Understand the effects of degree, leading coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2.
A3.5.3 Determine the maximum possible number of zeroes of a polynomial function, and understand the relationship between the x-intercepts of the graph and the factored form of the function.
Addressed HSCEs
The following Michigan High School Content Expectations will be addressed in this unit:
A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.
A1.1.3 Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities (e.g., differences of squares and cubes).
A1.2.1 Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve.
A1.2.2 Associate a given equation with a function whose zeros are the solutions of the equation.
A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.
A2.1.1 Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range.
A2.1.2 Read, interpret, and use function notation and evaluate a function at a value in its domain.
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.
A2.1.6 Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function, as x approaches positive or negative infinity, given the symbolic and graphical representations.
A2.1.7 Identify and interpret the key features of a function from its graph or its formula(e), (e.g. slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, average rate of change over an interval, and periodicity).
A2.2.1 Combine functions by addition, subtraction, multiplication, and division.
A2.2.2 Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x- and y-axes) to basic functions, and represent symbolically.
A2.2.3 Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs (e.g., f(x) = x3 and g(x) = x1/3).
A2.3.2 Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change.
A2.4.2 Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers.
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.
Sources
Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project