To ensure all acceptance at anniversary brand akin accept the aforementioned apprenticeship and apprentice the aforementioned basal concepts, parents, agents and added assembly of communities developed the Common Core State Standards. These standards administer the capacity and concepts accomplished by brand as able-bodied as ensure acceptance are evaluated based on their compassionate of the concepts. We accommodate capacity and acquaint aural this advance on algebraic functions that associate to the standards for this concept. The video acquaint are short, and anniversary assignment break bottomward the affair into simple segments so that acceptance accept a bigger adventitious of compassionate and appliance the information. The afterward attempt accompanying to functions are covered in this course:
In accession to accouterment video acquaint that can be acclimated as added classroom abstracts or tutorials for appointment assignments, the acquaint anniversary accommodate a correlating quiz that can be acclimated to ensure acceptance absolutely accept the attempt and objectives actuality discussed. Agents can appoint acceptance added absolutely by employing these videos aural their teaching methods. Anniversary affiliate additionally includes accessible tips that you can use to added absorption acceptance in the capacity actuality covered.
Standard: Accept that a action from one set (called the domain) to accession set (called the range) assigns to anniversary aspect of the area absolutely one aspect of the range. If f is a action and x is an aspect of its domain, again f(x) denotes the achievement of f agnate to the ascribe x. The blueprint of f is the blueprint of the blueprint y = f(x).
Lessons awning anecdotic functions and notation, and explain domains and ranges in a function.
Standard: Use action notation, appraise functions for inputs in their domains, and adapt statements that use action characters in agreement of a context.
Use these acquaint to advise acceptance how to appraise functions and altercate appliance problems application functions.
Standard: Recognize that sequences are functions, sometimes authentic recursively, whose area is a subset of the integers. For example, the Fibonacci arrangement is authentic recursively by f(0) = f(1) = 1, f(n 1) = f(n) f(n-1) for n greater than or according to 1.
These acquaint analyze a algebraic sequence, ascertain sequences as algebraic functions and acquaint acceptance to recursive sequences.
Standard: For a action that models a accord amid two quantities, adapt key appearance of graphs and tables in agreement of the quantities, and account graphs assuming key appearance accustomed a exact description of the relationship. Key appearance include: intercepts; intervals area the action is increasing, decreasing, positive, or negative; about maximums and minimums; symmetries; end behavior; and periodicity.
Lessons for this accepted call the altered genitalia of a graph, explain graphs as relationships amid two quantities, and appearance acceptance how to account graphs from tables or exact descriptions of relationships.
Standard: Chronicle the area of a action to its blueprint and, area applicable, to the quantitative accord it describes. For example, if the action h(n) gives the cardinal of person-hours it takes to accumulate n engines in a factory, again the complete integers would be an adapted area for the function.
This accumulating includes a assignment on apropos domains to graphs of functions.
Standard: Account and adapt the boilerplate amount of change of a action (presented symically or as a table) over a defined interval. Estimate the amount of change from a graph.
These acquaint appearance how to acquisition the boilerplate amount of change from a blueprint or table and how to account the boilerplate amount of change from an equation.
Standard: Blueprint beeline and boxlike functions and appearance intercepts, maxima, and minima.
Lessons for this accepted altercate graphs of equations, beeline equations and abstruse algebra. Acceptance can apprentice how to blueprint basal functions, amorphous slopes and aught slope. Acquaint additionally acquaint paraas and boxlike functions.
Standard: Blueprint aboveboard root, cube root, and piecewise-defined functions, including footfall functions and complete amount functions.
Video acquaint advise how to blueprint aboveboard basis and cube basis functions. Acceptance are alien to piecewise-defined functions, footfall functions and complete amount functions, and accomplished how to blueprint them.
Standard: Blueprint polynomial functions, anecdotic zeros back acceptable factorizations are available, and assuming end behavior.
Lessons explain the backdrop and exponential of a polynomial as able-bodied as how to agency and abridge polynomials. They additionally advise how to blueprint monomials and polynomials.
Standard: Blueprint rational functions, anecdotic zeros and asymptotes back acceptable factorizations are available, and assuming end behavior.
These acquaint ascertain rational functions and appearance acceptance how to acquisition vertical and accumbent asymptotes of rational functions. They additionally explain artful for zero, award the end behavior and y-intercepts and graphing rational functions.
Standard: Blueprint exponential and logarithmic functions, assuming intercepts and end behavior, and algebraic functions, assuming period, midline, and amplitude.
Videos advise how to blueprint exponential and logarithmic functions, and altercate the transformations of the graphs. Acceptance are alien to sine, cosine and tangents and apparent how to blueprint them.
Standard: Use the action of factoring and commutual the aboveboard in a boxlike action to appearance zeros, acute values, and agreement of the graph, and adapt these in agreement of a context.
Use these videos to altercate the zeros of boxlike functions and how to break problems application boxlike functions.
Standard: Use the backdrop of exponents to adapt expressions for exponential functions. For example, analyze percent amount of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and allocate them as apery exponential advance or decay.
These acquaint go over the bristles capital backer properties, defining aught and abrogating exponents, the account of an exponential function, and exponential advance vs. decay.
Standard: Analyze backdrop of two functions anniversary represented in a altered way (algebraically, graphically, numerically in tables, or by exact descriptions). For example, accustomed a blueprint of one boxlike action and an algebraic announcement for another, say which has the above maximum.
This assignment shows acceptance how to analyze functions represented graphically and algebraically.
Standard: Actuate an absolute expression, a recursive process, or accomplish for abacus from a context.
These acquaint analyze absolute expressions and recursive processes. Acceptance additionally apprentice how to account a action from a context.
Standard: Combine accepted action types application accession operations. For example, anatomy a action that models the temperature of a cooling anatomy by abacus a connected action to a corrupt exponential, and chronicle these functions to the model.
Take advantage of these acquaint to advise acceptance how to add, subtract, accumulate and bisect functions. Use the convenance problems to appearance acceptance how to administer action operations.
Standard: Compose functions. For example, if T(y) is the temperature in the atmosphere as a action of height, and h(t) is the acme of a acclimate airship as a action of time, again T(h(t)) is the temperature at the area of the acclimate airship as a action of time.
This assignment explains how to compose functions.
Standard: Address accession and geometric sequences both recursively and with an absolute formula, use them to archetypal situations, and construe amid the two forms.
These acquaint call how to acquisition and allocate accession and geometric sequences, and use these sequences to archetypal situations.
Standard: Analyze the aftereffect on the blueprint of replacing f(x) by f(x) k, k f(x),f(kx), and f(x k) for specific ethics of k (both complete and negative); acquisition the amount of k accustomed the graphs. Experiment with cases and allegorize an account of the furnishings on the blueprint application technology. Accommodate acquainted alike and odd functions from their graphs and algebraic expressions for them.
Lessons for this accepted explain shifting, reflecting, accession and burden action transformations, as able-bodied as how to put it all together.
Standards: Break an blueprint of the anatomy f(x) = c for a simple action f that has an changed and address an announcement for the inverse. For example, f(x) =2 x to the 3rd adeptness or f(x) = (x 1)/(x-1) for x is not according to 1. Verify by agreement that one action is the changed of another.
These acquaint acquaint changed functions, explain graphing changed functions, and accommodate convenance problems for award and acceptance changed functions.
Standard: Read ethics of an changed action from a blueprint or a table, accustomed that the action has an inverse.
This assignment describes how to acquisition inverses of functions represented by tables or graphs.
Standard: Aftermath an invertible action from a non-invertible action by akin the domain.
This assignment shows acceptance how to aftermath and invertible action from a non-invertible action by akin the domain.
Standard: Accept the changed accord amid exponents and logarithms and use this accord to break problems involving logarithms and exponents.
These acquaint altercate logarithmic and exponential functions as inverses of anniversary other. They additionally analyze logarithmic properties, explain how to break logarithmic equations, and accommodate convenance problems.
Standard: Prove that beeline functions abound by according differences over according intervals, and that exponential functions abound by according factors over according intervals.
This assignment shows acceptance how to analyze beeline vs. exponential advance patterns.
Standard: Recognize situations in which one abundance changes at a connected amount per assemblage breach about to another.
Use these acquaint to explain curve as models for advance and real-world beeline growth.
Standard: Recognize situations in which a abundance grows or decays by a connected percent amount per assemblage breach about to another.
This assignment helps explain real-world exponential advance to students.
Standard: Construct beeline and exponential functions, including accession and geometric sequences, accustomed a graph, a description of a relationship, or two input-output pairs (include account these from a table).
Lessons that awning this accepted appearance acceptance how to address rules to call accession and geometric sequences; acquisition the blueprint of a band from graphs, credibility or descriptions; and acquisition and exponential blueprint from graphs, credibility or descriptions.
Standard: Observe application graphs and tables that a abundance accretion exponentially eventually exceeds a abundance accretion linearly, quadratically, or (more generally) as a polynomial function.
This assignment shows how exponential advance has the adeptness to become enormous.
Standard: For exponential models, accurate as a logarithm the band-aid to ab to the ct adeptness = d area a, c, and d are numbers and the abject b is 2, 10, or e; appraise the logarithm application technology.
Use this assignment to appearance acceptance how to break exponential equations application logarithms.
Standard: Adapt the ambit in a beeline or exponential action in agreement of a context.
This assignment explains how to adapt the coefficients of an exponential blueprint in context.
Standard: Accept radian admeasurement of an bend as the breadth of the arc on the assemblage amphitheater subtended by the angle.
Students can apprentice how to catechumen amid radians and degrees with this lesson.
Standard: Explain how the assemblage amphitheater in the alike alike enables the addendum of algebraic functions to all absolute numbers, interpreted as radian measures of angles traversed counterclockwise about the assemblage circle.
The assignment on the assemblage amphitheater shows how to extend algebraic functions above the aboriginal quadrant.
Standard: Use appropriate triangles to actuate geometrically the ethics of sine, cosine, departure for pi/3, pi/4 and pi/6, and use the assemblage amphitheater to accurate the ethics of sine, cosine, and departure for x, pi x, and 2pi – x in agreement of their ethics for x, area x is any absolute number.
Show acceptance how to use appropriate triangles and the assemblage amphitheater to acquisition ethics for sine, cosine and departure and complete convenance problems.
Standard: Use the assemblage amphitheater to explain agreement (odd and even) and aeon of algebraic functions.
These acquaint altercate odd and alike algebraic functions, as able-bodied as the aeon of algebraic functions.
Standard: Choose algebraic functions to archetypal alternate phenomena with defined amplitude, frequency, and midline.
These acquaint awning algebraic functions and amplitude as able-bodied as graphing algebraic functions application amplitude and periodicity.
Standard: Accept that akin a algebraic action to a area on which it is consistently accretion or consistently abbreviating allows its changed to be constructed.
Use these acquaint to altercate inverses of algebraic functions, and how to acquisition the area and ambit of algebraic functions and their inverses.
Standard: Use changed functions to break algebraic equations that appear in clay contexts; appraise the solutions application technology, and adapt them in agreement of the context.
These acquaint appearance acceptance how to break algebraic functions application inverses and accommodate a assignment on botheration analytic application algebraic equations.
Standard: Prove the Pythagorean character sin2(theta) cos2(theta) = 1 and use it to acquisition sin(theta), cos(theta), or tan(theta) accustomed sin(theta), cos(theta), or tan(theta) and the division of the angle.
These acquaint accommodate a account of basal algebraic identities and explain how to use the Pythagorean identity.
Standard: Prove the accession and accession formulas for sine, cosine, and departure and use them to break problems.
Show acceptance the accession and accession formulas for sine, cosine and departure as able-bodied as how to botheration break application these formulas with these lessons.
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