{"id":112,"date":"2019-12-02T12:55:57","date_gmt":"2019-12-02T17:55:57","guid":{"rendered":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/?p=112"},"modified":"2019-12-02T13:41:46","modified_gmt":"2019-12-02T18:41:46","slug":"standards-for-first-semester","status":"publish","type":"post","link":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/2019\/12\/02\/standards-for-first-semester\/","title":{"rendered":"Standards for first semester"},"content":{"rendered":"\n<p>In this topic, students will:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Recognize that sequences are functions with integer domains<\/li><li>Recognize arithmetic sequences<\/li><li>Connect arithmetic sequences with linear functions<\/li><li>Identify common differences and find specified terms for arithmetic sequences<\/li><li>Recognize geometric sequences<\/li><li>Connect geometric sequences to exponential functions<\/li><li>Identify common ratios and find specified terms for geometric sequences<\/li><li>Write recursive and explicit definitions for the\u00a0<em>n<\/em>th term in an arithmetic or geometric sequence<\/li><li>Find sums for finite arithmetic and geometric series<\/li><li>Use arithmetic and geometric sequences and series to model real-world situations<\/li><li>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;<\/li><li> Recognize that the inverse of a relation is the set of ordered pairs obtained by interchanging the coordinates in each ordered pair<\/li><li>Understand the graphical, tabular, and algebraic relationship between a linear function and its inverse<\/li><li>Understand the relationship between exponential and logarithmic functions<\/li><li>Understand the relationship between quadratic and square root functions<\/li><li>Represent the inverse of a function using function notation<\/li><li>Identify one-to-one functions<\/li><li>Restrict the domain of a quadratic function in order for its inverse to be a function<\/li><li>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;<\/li><li> Apply transformations to graphs of parent functions<\/li><li>Recall key features of the linear, exponential, quadratic, and absolute value functions<\/li><li>Describe a relationship based on its graph<\/li><li>Recognize the general form of a quadratic equation and explain how the values of\u00a0<em>a<\/em>,\u00a0<em>h<\/em>, and\u00a0<em>k<\/em>\u00a0affect the shape of the parabola<\/li><li>Describe and use the transformation from one function to another in terms of vertical shifts, vertical shrinks\/stretches, and horizontal shifts<\/li><li>Recognize that a piecewise function is made up of pieces of more than one function<\/li><li>Generalize the transformations of all functions based on the values of\u00a0<em>a<\/em>,\u00a0<em>h<\/em>, and\u00a0<em>k<\/em><\/li><li>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;<\/li><li> Recognize the general form of a polynomial function<\/li><li>Identify the degree of a polynomial<\/li><li>Perform mathematical operations on polynomial expressions<\/li><li>Build polynomial functions from linear and quadratic functions<\/li><li>Describe the increasing and decreasing behavior of quadratic and cubic functions<\/li><li>Identify absolute and relative maximum and minimum values of quadratic and cubic functions<\/li><li>Describe the domain and range of cubic functions<\/li><li>Identify odd and even functions from graphs using symmetry<\/li><li>Calculate average rates of change for quadratic and cubic functions <\/li><li> Describe the concavity of the graph of a polynomial function<\/li><li>Use interval notation to describe a set of values<\/li><li>Understand the relationship between the degree of a polynomial and the number of real zeros it has<\/li><li>Understand the relationship between the degree of a polynomial function and the number of local extreme values of the function<\/li><li>Describe the end behavior of polynomials of odd and even degree<\/li><li>Use polynomial functions to model real-world situations <\/li><li> Describe the concavity of the graph of a polynomial function<\/li><li>Use interval notation to describe a set of values<\/li><li>Understand the relationship between the degree of a polynomial and the number of real zeros it has<\/li><li>Understand the relationship between the degree of a polynomial function and the number of local extreme values of the function<\/li><li>Describe the end behavior of polynomials of odd and even degree<\/li><li>Use polynomial functions to model real-world situations <\/li><li> Analyze situations modeled by polynomial equations<\/li><li>Define and use imaginary and complex numbers in the solution of quadratic equations<\/li><li>Use the discriminant of a quadratic equation to determine the number and type of roots of the equation<\/li><li>Use polynomial long division and synthetic division to solve problems<\/li><li>Factor the sum and difference of two cubes<\/li><li>Factor polynomial expressions by grouping<\/li><li>Solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems<\/li><li>Understand the implications of the Fundamental Theorem of Algebra and the Remainder Theorem <\/li><li>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/li><li> Perform operations on rational expressions<\/li><li>Build rational functions from rational expressions<\/li><li>Simplify rational expressions by factoring<\/li><li>Interpret models of rational functions<\/li><li>Demonstrate transformations of functions on rational functions using parameter changes<\/li><li>Find vertical asymptotes and removable discontinuities of rational functions<\/li><li>Analyze the limiting or end behavior of functions and see how this behavior leads to horizontal asymptotes<\/li><li>Find the domain and range of rational functions and restrict these for problem situations<\/li><li>Move between the quotient form and the transformation form of a rational function <\/li><li> Write rational equations to model problem situations<\/li><li>Solve rational equations using graphs, tables, and analytic strategies<\/li><li>Interpret solutions to rational equations in context using appropriate mathematical vocabulary<\/li><li>Identify extraneous solutions <\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In this topic, students will: Recognize that sequences are functions with integer domainsRecognize arithmetic sequencesConnect arithmetic sequences with linear functionsIdentify common differences and find specified terms for arithmetic sequencesRecognize geometric sequencesConnect geometric sequences to exponential functionsIdentify common ratios and find specified terms for geometric sequencesWrite recursive and explicit definitions for the\u00a0nth term in an arithmetic&#8230; <\/p>\n<div class=\"read-more\"><a href=\"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/2019\/12\/02\/standards-for-first-semester\/\">Read More<\/a><\/div>\n","protected":false},"author":2248,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-112","post","type-post","status-publish","format-standard","hentry","category-blogs"],"_links":{"self":[{"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/posts\/112","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/users\/2248"}],"replies":[{"embeddable":true,"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/comments?post=112"}],"version-history":[{"count":2,"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/posts\/112\/revisions"}],"predecessor-version":[{"id":114,"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/posts\/112\/revisions\/114"}],"wp:attachment":[{"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/media?parent=112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/categories?post=112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iblog.dearbornschools.org\/hewittalgebra2honors\/wp-json\/wp\/v2\/tags?post=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}