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Functions #

Year 8

Identifying Relations [3496]
Identifying Functions [3497]
Identifying if given relations are functions [3498]
Identifying domain of a function [3500]
Identifying range of a function [3501]
Types of functions [3502]
Identifying increasing functions [3506]
Identifying decreasing functions [3507]
Defining sets [3530]
Cardinality of sets [3531]
Types of sets [3532]
Illustrates union of events [3533]
Illustrates intersection of events [3534]
Illustrates mutually exclusive events [3535]
Properties of complementary sets [3537]
Computing probability of mutually exclusive events [3538]
Definition of terms (point, line, plane) [3540]
Describing a point [3541]

Year 10

Defining Polynomial Functions [2972]
Identifying domain of polynomial functions [2973]
Identifying range of polynomial functions [2974]
Evaluating Polynomial Functions [2975]
Graphing Polynomial Functions [2976]
Solving Problems involving Polynomial Functions [2977]
Defining Hyperbolic Functions [2978]
Identifying Domain of Hyperbolic Functions [2979]
Identifying Range of Hyperbolic Functions [2980]
Evaluating Hyperbolic Functions [2981]
Graphing Hyperbolic Functions [2982]
Solving Problems involving Hyperbolic Functions [2983]
Classifying polynomials [2984]
Addition of Monomials [2985]
Subtraction of Monomials [2986]
Multiplying a monomial and a binomial [2988]
Determining roots of polynomials using Synthetic Division [3001]
Defining functions: mixed review [3004]
Identifying Domain of a function [3005]
Find the domain of the function from the graph [3006]
Find the domain of the function from the set of ordered pairs [3008]
Identifying Range of a function [3009]
Find the Range of the function from the graph [3010]
Find the Range of the function from the set of ordered pairs [4450]
Domain and range of function from the graph [4452]
Domain and range of function from the set of ordered pairs [4453]
Find values using function graphs [4454]
Find values using function equations [3017]
Evaluation of functions [3018]
Operations on functions addition [3019]
Operations on functions subtraction [4455]
Operations on functions multiplication [3021]
Operations on functions division [3022]
Composition of Functions [3023]
Identify types of functions from graphs [3024]
Identify types of functions from equations [3025]
Find the Range of the function from the set of ordered pairs [3012]
Identify linear, affine, quadratic, and cubic functions from graphs [3026]
Identify affine, quadratic, rational and radical functions from graphs [3027]
Identify sine, cosnie, and absolute value functions from graphs [3028]
Identify linear, affine, quadratic, and cubic functions from tables [3029]
Identify linear, quadratic, rational and radical functions from tables [3030]
Identify sine, cosnie, and absolute value functions from tables [3031]
Write linear, affine, quadratic, and cubic functions [3032]
Write linear, quadratic, rational and radical functions [3033]
Write sine, cosnie, and absolute value functions [3034]
Increasing functions [3035]
Decrease functions [3036]
Constante functions [3037]
Identify increase, Increase and constant intervals (Refrence function) [3038]
Finding the Maximum Values of a Function [3039]
Symmetric Functions [3042]
Even functions [3043]
Odd function [3044]
Periodic function [3045]
Identify quadratic function from the equation [3046]
Identify quadratic function from the graph [3047]
Identify quadratic function from the table [3048]
Range of quadratic function [4456]
Complete a function table from the equation of quadratic function [3052]
Complete a function table from the graph of quadratic function [3053]
Write quadratic function to solve word problems [3054]
Solving Problems involving quadratic Functions [3055]
Compare quadratic function: graphs, tables and equations [3056]
Write equations in standard form from tables, grahs and mappings and lists of points [3057]
Evaluating quadratic Functions [3058]
Quadratic function over unit intervals [3059]
Identify increase, Increase and constant intervals [3060]
Identify rational function from the equation [3062]
Identify rational function from the graph [3063]
Identify rational function from the table [3064]
Identify quadratic function from set of ordered pairss [3068]
Domain of rational functions [3069]
Range of rational function [3070]
Complete a function table from the equation of rational function [3071]
Complete a function table from the graph of rational function [3072]
Write rational function to solve word problems [3073]
Solving Problems involving rational Functions [3074]
Compare rational function: graphs, tables and equations [3075]
Write equations of rational function in standard form from tables, grahs and mappings and lists of points [3076]
Evaluating rational Functions [3077]
Rational function over unit intervals [3078]
Identify increase, Increase and constant intervals of rational Function [3079]
Rational function Properties [3080]
Identify cubic function from the equation [3081]
Identify cubic function from the graph [3082]
Identify cubic function from the table [3083]
Identify cubic function from set of ordered pairs [3084]
Domain of cubic function [3085]
Range of cubic function [3086]
Complete a function table from the equation of cubic function [3087]
Complete a function table from the graph of cubic function [3088]
Write cubic function to solve word problems [3089]
Solving Problems involving cubic Functions [3090]
Compare cubic function: graphs, tables and equations [3091]
Write equations of cubic function in standard form from tables, grahs and mappings and lists of points [3092]
Evaluating cubic Functions [3093]
Cubic function over unit intervals [3094]
Identify increase, Increase and constant intervals of cubic function [3095]
Cubic function Properties [3096]
Identify radical function from the equation [3097]
Identify radical function from the graph [3098]
Identify radical function from the table [3099]
Identify radical function from set of ordered pairs [3100]
Domain of radical function [3101]
Range of radical function [3102]
Complete a function table from the equation of radical function [3103]
Write radical function to solve word problems [4457]
Solving Problems involving radical Functions [4458]
Compare radical function: graphs, tables and equations [4459]
Write equations in standard form from tables, grahs and mappings and lists of points [3108]
Evaluating radical Functions [3109]
Radical function over unit intervals [3110]
Identify increase, Increase and constant intervals of radical function [3111]
Radical function Properties [3112]
Solving Problems involving cosine Functions [4460]
Compare cosine function: graphs, tables and equations [4461]
Write equations in standard form from tables, grahs and mappings and lists of points [4462]
Identify absolute value function from the equation [3113]
Identify absolute value function from the graph [3114]
Identify absolute value function from the table [3115]
Identify absolute value function from set of ordered pairs [3116]
Domain of absolute value function [3117]
Range of absolute value function [3118]
Complete a function table from the equation of absolute value function [3119]
Complete a function table from the graph of absolute value function [3120]
Write absolute value function to solve word problems [3121]
Solving Problems involving absolute value Functions [3122]
Compare absolute value function: graphs, tables and equations [3123]
Write equations in standard form from tables, grahs and mappings and lists of points [3124]
Evaluating absolute value Functions [3125]
Absolute value function over unit intervals [3126]
Identify increase, Increase and constant intervals of absolute value function [3127]
Absolute value function Properties [3128]
Identify sine function from the equation [3129]
Identify sine function from the table [3131]
Identify sine function from the table [3130]
Identify sine function from set of ordered pairs [3132]
Domain of sine function [3133]
Range of sine function [3134]
Complete a function table from the equation of quadratic function [3135]
Complete a function table from the graph of sine function [3136]
Write sine function to solve word problems [3137]
Solving Problems involving sine Functions [3138]
Compare sine function: graphs, tables and equations [3139]
Write equations of sine function in standard form from tables, grahs and mappings and lists of points [3140]
Evaluating sine Functions [3141]
Sine function over unit intervals [3142]
Identify increase, Increase and constant intervals of sine function [3143]
Sine function Properties [3144]
Identify cosine functions from the equation [3145]
Identify cosine function from the graph [3146]
Identify cosine function from the table [3147]
Identify cosine function from set of ordered pairs [3148]
Domain of cosine function [3149]
Range of cosine function [3150]
Complete a function table from the equation of cosine function [3151]
Complete a function table from the graph of cosine function [3152]
Write cosine function to solve word problems [3247]
Evaluating Cosine Functions [3251]
Cosine function over unit intervals [4463]
Identify Decrease, Increase and constant intervals [4464]
Cosine function Properties [4465]
Graph sine functions [3322]
Graph sine and cosine functions [3324]

Year 11

Function types: mixed review [3680]
Reference function: mixed review (domains, ranges, graphs, function properties) [3701]
Use Function Notation to evaluate functions [3682]
The average rate of change [3683]
Find the Rate of Change over a given interval [3684]
The direction of variation of reference functions [3685]
The table of variation of reference functions [3686]
The sing of reference functions [3687]
Graphing functions using reference functions [3688]
Identify Piecewise-defined function from the graph [3690]
Create and use a Piecewise-defined function from real world data [3698]
Step Functions [3700]
Polynomial functions: mixed review (domains, ranges, graphs, function properties) [3773]
Degree of a polynomial functions: mixed review [3774]
Polynomial functions equality [3775]
Add polynomial functions [3776]
Subtract polynomial functions [3777]
Multiply polynomial functions [3778]
Mixed polynomial functions operations [3779]
Mixed polynomial functions operations: word problems [3780]
Simplify polynomial functions [3781]
Identify the root of a polynomial functions [3783]
Find the root of a polynomial functions [3784]
Graph the root of a polynomial functions [3785]
Root of a polynomial functions: word problems [3786]
Factorizing polynomial functions using the factor (x-a) [3787]
Factorizing polynomial functions using roots [3788]
Direct Variation [3870]
Inverse Variation [3871]
Variation Function (ƒ + k) [3873]
Understanding Limit Notation [3905]
Use The Formal Definition Of Limit [3906]
Understanding The Limits Of Functions [3907]
Understanding Left-Hand Limits And Right-Hand Limits [3908]
Learn That A Limit Can Fail To Exist Because Of Unbounded Behavior [3911]
Limits And Oscillating Behavior [3912]
Evaluating Limits Using The Limit Notation ( Estimate A Limit Using A Numerical Approach) [3913]
One-Sided Limits [3916]
Determine Infinite Limits From The Left [3918]
Determine Infinite Limits From The Right [3919]
Finite And Infinite Limits [3921]
Finite Limit And Infinite Limit At A Real Number [3922]
Evaluate Basic Limits [3924]
Limit Of A Polynomials [3925]
Limit Of A Rational Function [3926]
Limit Of The Sum Of Two Function [3927]
Limit Of The Product Of Two Function [3928]
Limit Of The Ratio Of Two Function [3929]
Limits Of | F(X) | [3931]
Limits Of √F(X) [3932]
Evaluate Limits Of Function (Limits Of Sum , Product And Composition Of Function) [3933]
Understanding The Asymptote [3935]
The Vertical Asymptote [3936]
The Horizontal Asymptote [3937]
The Oblique Asymptote [3938]
The Vertical, Horizontal And Oblique Asymptote [3939]
Graph The Asymptote [3940]
Prove That The Line Is The Asymptote To The Curve Of The Function [3941]
Find The Asymptote To The Curve Of The Function [3942]
The Relative Position Of The Asymptote To The Curve Of The Function [3943]
Continuity On A Closed Interval [3950]
Continuity At A Point [3951]
Properties Of Continuity [3952]
Continuity Theorem [3953]
Properties Of Continuous Functions [3954]
Understanding Average Rate Of Change [3956]
The Average Rate Of Change Formula [3957]
Find The Average Rate Of Change Of A Function [3958]
Find The Average Rate Of Change From The Graph [3959]
Find The Average Rate Of Change From Equation [3960]
Find Instantaneous Rates Of Change [3961]
Velocity As A Rate Of Change [3962]
The Real Limit Of Function When X = 0 [3963]
Identify The Derivative Function Of The Function Ƒ [3964]
Find The Derivative Function Of The Function Ƒ [3965]
The Domain Of Derivability [3967]
The Relationship Between A Function And Its Derived Function [3968]
Geometric Interpretation Of The Derived Number [3969]
The Tangent Equation [3971]
The Tangent Slope [3972]
The Tangent To A Parabola [3973]
The Tangent To A Hyperbola [3974]
The Tangent To A Parabola Or A Hyperbola [3975]
Introduction To Linear Approximations [3977]
Determine The Linear Approximation [3978]
Approximation Of A Function Around X = 0 [3979]
Approximation Of A Function Around X = A (A Is A Real Number) [3980]
Linearization Of Radical Functions [3981]
Linearization Of Polynomial Functions [3982]
Linearization Of Rational Functions [3983]
Linearization Of Exponential Functions [3984]
Linearization Of Logarithmic Functions [3985]
Linearization Of Trigonometric Functions [3986]
Exponential Function: Mixed Review (Domains, Ranges, Graphs, Function Properties) [4287]
Key Features Of Exponential Functions By Graphs [4288]
Key Features Of Exponential Functions By Tables [4289]
Key Features Of Exponential Functions By Equations [4290]
Use Compound Interest Formula For Fixed Amount Of Time Compounding (Annual, Semi-Annual, Monthly, Etc) [4297]
Use Compound Interest Formula For Continuous Compounding [4298]
Use Compound Interest Formula To Solve For T (Time) [4299]
Exponential Growth And Decay: Word Problems [4302]
Limit Of Exponential Function [4303]
Rewrite Exponential Functions Into Logarithmic Functions [4307]
Rewrite Logarithmic Functions Into Exponential Functions [4308]
Evaluate Natural Logarithms (With And Without Technology) [4310]
Key Features Of Logarithmic Functions By Graphs [4312]
Key Features Of Logarithmic Functions By Tables [4313]
Key Features Of Logarithmic Functions By Equations [4314]
Limit Of Logarithmic Function [4319]
Find The Measure Of Directed Angle [4405]
The Derivative Of The Sum Of Two Functions [4267]
The Derivative Function Of The Product Of Two Functions [4268]
The Derivative Function Of The Reciprocal Of A Function [4269]
The Derivative Function Of The Ratio Of Two Functions [4270]
The Derivative Function Of The Function Ƒ(X) = U(Ax + B) [4271]
Basic Derivative Rules [4272]
Functions That Have The Same Derivative [4273]

Year 12

Understanding primitive function [3705]
Primitive function of a given function [3706]
The notation for primitive functions [3707]
"Antiderivative" and "Indefinite integral" as synonyms for primitive function [3708]
Properties of primitive function [3709]
Primitive function and continuity [3710]
Primitive functions of elementary functions [3711]
Methods for computing primitive functions [3712]
Calculate a primitive function using the table of usual antiderivatives [3713]
Calculate antiderivatives of the usual functions [3714]
Antiderivatives rules (sum, difference and constan rule) [3715]
Antiderivative power rule [3716]
Calculate the antiderivatives of the addition [3729]
Calculate antiderivatives of a subtraction [3718]
Calculate antiderivatives of a rational fraction [3719]
Calculate the antiderivatives of composed functions [3721]
Calculate the antiderivative using integration by parts [3722]
Antiderivative of trig functions [3724]
Antiderivative of exponential function [3725]
Calculate primitive function of function that takes the value y0 at x0 [3726]
Graphing the primitive function [3728]
Understanding integration [3730]
Fundamental theorems of integral calculus [3731]
Types of integrals (definite integral and indefinite integral) [3732]
Properties of integral calculus [3733]
Integral calculus formulas [3734]
Methods to find integrals [3735]
Finding integrals by integration by parts [3736]
Finding integrals by substitution method [3737]
Finding integrals by integration by partial fractions [3738]
Interpretation geometries of integration [3739]
Application of integral calculus [3740]
Find accumulation of changes in the function [3741]
Find average change [3742]
Calculate the area [3743]
Calculate the distance [3744]
Calculate the volumes [3745]
Calculate the surface area of revolution [3746]
Calculate the volume of revolution [3747]
Differentiation of Logarithmic Functions [3764]
Understanding differential [3749]
Derivative of function as limits [3750]
Differentiation formulas [3751]
Interpretation geometries of differentiation [3752]
Understanding Differentiation Rules [3755]
Product Rule [3757]
Quotient Rule [3758]
Chain Rule [3759]
Differentiation of Elementary Functions [3760]
Differentiation of Trigonometric Functions [3761]
Differentiation of Special Functions [3763]
The second derivative [3766]
Real-Life Applications of Differentiation [3767]
Understand the relationship between differentiability and continuity [3768]
Distinguish between functions written in implicit form and explicit form [3769]
Use implicit differentiation to find the derivative of a function [3770]
Identify Tangent Functions From The Equation [4109]
Identify Tangent Functions From The Graph [4110]
Identify Tangent Functions From The Table [4111]
Identify Tangent Functions From A Set Of Ordered Pairs [4112]
Domain Of Tangent Functions [4113]
Range Of Tangent Functions [4114]
Complete A Function Table From The Graph Of A Tangent Function [4115]
Write Tangent Functions To Solve Word Problems [4116]
Solve Problems Involving Tangent Functions [4117]
Evaluate Tangent Functions [4118]
Identify Increasing, Decreasing And Constant Intervals Of Tangent Functions [4119]
Determine the period from a sine or cosine function in equation form [4121]
Determine The Amplitude From A Sine Or Cosine Function In Equation Form [4122]
Determine The Period From A Sine Or Cosine Function In Graph Form [4123]
Determine The Amplitude From A Sine Or Cosine Function In Graph Form [4124]
Identify Minimum And Maximum Points Of Sine And Cosine Equations [4125]
Identify Symmetry In The Graphs Of Sine And Cosine [4126]
Graph Sine And Cosine Functions Using Transformations [4127]
Determine The Asymptotes From A Tangent Function In Equation Form [4128]
Determine The Asymptotes From A Tangent Function In Graph Form [4129]
Graph A Tangent Function [4130]
Identify Symmetry In Tangent Graphs [4131]
Graph A Tangent Function Using Transformations [4132]
Determine If Trig Functions Are Odd, Even, Or Neither [4133]
Identify Cosecant Functions From The Equation [4135]
Identify Cosecant Functions From The Graph [4136]
Identify Cosecant Functions From A Set Of Ordered Pairs [4138]
Domain Of Cosecant Functions [4139]
Range Of Cosecant Functions [4140]
Identify Secant Functions From The Equation [4142]
Identify Secant Functions From The Graph [4143]
Identify Secant Functions From A Set Of Ordered Pairs [4145]
Domain Of Secant Functions [4146]
Range Of Secant Functions [4147]
Identify Cotangent Functions From The Equation [4149]
Identify Cotangent Functions From The Graph [4150]
Identify Cotangent Functions From A Set Of Ordered Pairs [4152]
Domain Of Cotangent Functions [4153]
Range Of Cotangent Functions [4154]
Graph A Cosecant Function [4156]
Graph A Secant Function [4157]
Determine The Period From A Cosecant Or Secant Function In Equation Form [4158]
Determine The Period From A Cosecant Or Secant Function In Graph Form [4159]
Determine The Asymptotes For A Cosecant Function In Equation Form [4160]
Determine The Asymptotes For Secant Function In Equation Form [4161]
Determine The Asymptotes For A Cosecant Function In Graph Form [4162]
Determine The Asymptotes For Secant Function In Graph Form [4163]
Identify Symmetry In Cosecant Graphs [4164]
Identify Symmetry In Secant Graphs [4165]
Graph A Cotangent Function [4166]
Determine The Period From A Cotangent Function In Equation Form [4167]
Determine The Period From A Cotangent Function In Graph Form [4168]
Determine The Asymptotes From A Cotangent Function In Equation Form [4169]
Determine The Asymptotes From A Cotangent Function In Graph Form [4170]
Identify Symmetry Of Cotangent Graphs [4171]
Determine If Reciprocal Trig Functions Are Odd, Even, Or Neither [4172]
Understand That Arcsine, Arccosine, And Arctangent Represent The Inverse Of A Sine, Cosine, And Tangent Function Respectively [4174]
Evaluate Arcsine Functions Using Unit Circle Knowledge [4175]
Evaluate Arcsine Functions Using A Calculator [4176]
Graph The Arcsine Functions [4177]
Evaluate Arccosine Functions Using Unit Circle Knowledge [4178]
Evaluate Arccosine Functions Using A Calculator [4179]
Graph Arccosine Functions [4180]
Domain Of Arcsine And Arccosine Functions [4181]
Range Of Arcsine Functions [4182]
Range Of Arccosine Functions [4183]
Evaluate Arctangent Functions Using Unit Circle Knowledge [4184]
Evaluate Arctangent Functions Using A Calculator [4185]
Graph Arctangent Functions [4186]
Domain Of Arctangent Functions [4187]
Range Of Arctangent Functions [4188]
Properties Of Inverse Trig Functions [4189]
Use Reciprocal Identities To Evaluate Trig Functions [4191]
Use Quotient Identities To Evaluate Trig Functions [4192]
Use Pythagorean Identities To Evaluate Trig Functions [4193]
Use Cofunction Identities To Evaluate Trig Functions [4194]
Use Even/Odd Identities To Evaluate Trig Functions [4195]
Simplify A Trigonometric Expression Using Trig Identities [4196]
Add And Subtract Trigonometric Expressions Using Trig Identities [4198]
Trigonometric Substitution [4200]
Rewrite A Logarithmic Expression Using Trig Identities [4201]
Verify Trigonometric Identities [4202]
Use The Sum And Difference Formulas For Sine To Evaluate A Trigonometric Function [4204]
Use The Sum And Difference Formulas For Tangent To Evaluate A Trigonometric Function [4206]
Use Sum And Difference Formulas To Verify Identities [4207]
Use Sum And Difference Formulas To Solve A Trigonometric Equation [4208]
Use Multiple-Angle Formulas To Rewrite Trigonometric Functions [4209]
Use Multiple-Angle Formulas To Evaluate Trigonometric Functions [4210]
Use Double-Angle Formulas To Rewrite Trigonometric Functions [4211]
Use Double-Angle Formulas To Evaluate Trigonometric Functions [4212]
Use Power-Reducing Formulas To Rewrite Trigonometric Functions [4213]
Use Half-Angle Formulas To Rewrite Trigonometric Functions [4214]
Use Half-Angle Formulas To Evaluate Trigonometric Functions [4215]
Use Product-To-Sum Formulas To Rewrite Trigonometric Functions [4216]
Use Product-To-Sum Formulas To Evaluate Trigonometric Functions [4217]
Use Sum-To-Product Formulas To Rewrite Trigonometric Functions [4218]
Use Sum-To-Product Formulas To Evaluate Trigonometric Functions [4219]
Use Trigonometric Formulas To Rewrite Real Life Models [4220]
Solve A Right Triangle For Any Missing Sides Using Trigonometry [4226]
Solve A Right Triangle For Any Missing Angles Using Trigonometry [4222]
Find An Angle Of Depression [4227]
Find Directions In Terms Of Bearings [4228]
Simple Harmonic Motion [4223]
Combining Like Terms Using Trigonometric Functions [4224]
Extract Square Roots From Trigonometric Equation [4225]
Solve Trigonometric Equations Of Quadratic Type [4229]
Squaring And Converting To Quadratic Types [4231]
Use The Quadratic Formula To Solve Trigonometric Equations Of Quadratic Type [4232]
Use Inverse Functions To Solve Trigonometric Equations Of Quadratic Type [4233]
Solving A Multiple-Angle Equation [4234]
Estimate A Limit Using A Numerical Approach [4602]
Estimate A Limit Using A Graphical Approach [4603]
Estimate A Limit Using An Analytic Approach [4604]
Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left [4605]
Learn That A Limit Can Fail To Exist Because Of Unbounded Behavior [4606]
Limits And Oscillating Behavior [4607]
Use A Formal Definition Of Limit [4608]
Evaluate Basic Limits [4609]
Limit Of A Polynomial [4610]
Limit Of A Rational Function [4611]
Limit Of A Composite Function [4612]
Limits Of Trigonometric Functions [4613]
Evaluate A Limit Using The Dividing Out Technique [4614]
Determine Infinite Limits From The Right [4624]
Use Vertical Asymptotes To Help In Determining Limits [4625]

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