The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. Prerequisite/Extension SOL 7.13 a) verbal expressions as algebraic expressions and sentences as equations and vice versa; b) evaluate algebraic expressions 8.1 a) simplify numerical expressions 8.4 evaluate algebraic expressions using order of operations A.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables 7.12 represent relationships with tables, graphs, rules, and words 8.17 ID domain, range 8.14 make connections between any two representations A.7 investigate/analyze function families and characteristics a)determine relation is function; b)domain/range; c) zeros; d) x‐ and y intercepts; e) find values of functions for elements in domain; f) make connect between/among multiple representations of functions •A function can be described on an interval as increasing, decreasing, or constant. •End behavior describes a function as x approaches positive and negative infinity. •A zero of a function is a value of x that makes equal zero. •Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically. •Given the graph of a function, identify intervals on which the function is increasing and decreasing. •Describe the end behavior of a function. The Fundamental Theorem of Algebra states that, including complex and repeated solutions, an nth degree polynomial equation has exactly n (solutions). The following statements are equivalent: k is a zero of the polynomial function f; (x – k) is a factor of f(x); k is a solution of the polynomial equation f(x) = 0; and k is an x-intercept for the graph of y = f(x). •Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. •Define a polynomial function, given its zeros. •Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. •For a function, identify of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function. a polynomial equation, determine the number of real solutions and nonreal solutions. Performance Task must be completed and graded on rubric by the end of Quarter 2
Sample Performance Tasks: SOL AII.6 & AII.7 Students determine how many feet of cable are necessary to connect two towers of a suspension bridge. Dates Standards/Essential Questions Essential Knowledge/Skills/Understanding Resources Third Quarter Standard A2.6 The student will recognize the general of function (exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. A2.7a, b, c, d, e, f, g The student will investigate and analyze functions algebraically and graphically. Key concepts include domain and range, including limited domains and ranges; x- and y-intercepts; increasing or decreasing intervals; asymptotes; end behavior; inverse of a function. Graphing calculators will be used as a tool to assist in investigation of functions. Prerequisite/Extension SOL 7.12 represent relationships with tables, graphs, rules, and words •The graphs/equations for a family of functions can be determined a transformational approach. •Transformations of graphs include translations, reflections, and dilations. •A parent graph is an anchor graph from which other graphs are derived with transformations. •Recognize graphs of parent functions. •Given a transformation of a parent function, identify the graph of the transformed function. •Given the equation and using a transformational approach, graph a function. •Given the graph of a function, identify the parent function. the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image. •Using a transformational approach, write the equation of a function given its graph. •A function can be described on an interval as increasing, decreasing, or constant. •Asymptotes may describe both local and global behavior of functions. •End behavior describes a function as x approaches positive and negative infinity. •If (a, b) is an element of a function, then (b, a) is an element of the inverse of the function. •Exponential and logarithmic functions are inverses of each Key Vocabulary Exponent Asymptote DOE Lesson Textbook Resources Pearson 7-1, 7-2, 7-3 Resources/Lessons
Standards/Essential Questions Essential Knowledge/Skills/Understanding Resources Fourth Quarter ALL SOL’s Review Key Vocabulary DOE Lesson Plans Textbook Resources Resources/Lessons 25 days or until the end of year Extra Topics Including but not limited to: Trigonometry Systems of Linear Equations (Matrices) Sections Resources/Lessons Performance Task must be completed and graded on rubric by the end of Quarter 4 Sample Performance Tasks: