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- Common Core MathK - 8High School

2139 questions103 skills

215 questions10 skills

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If *f* is a function and *x* is an element of its domain, then *f*(*x*) denotes the output of *f* corresponding to the input *x*. The graph of *f* is the graph of the equation *y* = *f*(*x*).

Range of quadratic functions

Recognize functions from graphs

Function rules from equations

Domain of advanced functions

Domain of advanced piecewise functions

Function inputs & outputs: graph

Evaluate functions from their graph

Function inputs & outputs: equation

Evaluate function expressions

Recognize functions from tables

176 questions11 skills

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Evaluate functions

Function notation word problems

Function inputs & outputs: graph

Use geometric sequence formulas

Evaluate piecewise functions

Use arithmetic sequence formulas

Evaluate sequences in recursive form

Evaluate functions from their graph

Function inputs & outputs: equation

Evaluate function expressions

Evaluate step functions

95 questions5 skills

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

177 questions8 skills

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. *Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity*.

46 questions3 skills

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

76 questions3 skills

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

756 questions41 skills

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Positive & negative intervals of polynomials

Graphs of exponential functions

Rational function points of discontinuity

Slope from two points

Relative maxima and minima

Slope from equation

Graphs of logarithmic functions

Amplitude of sinusoidal functions from equation

Graph absolute value functions

Slope-intercept intro

Zeros of polynomials (factored form)

Midline of sinusoidal functions from graph

Graph from slope-intercept form

Graph quadratics in vertex form

End behavior of rational functions

Evaluate piecewise functions

Positive and negative intervals

Intercepts from an equation

Increasing and decreasing intervals

Analyze vertical asymptotes of rational functions

Graphs of nonlinear piecewise functions

Graphing linear relationships word problems

Graph quadratics in standard form

Graphs of square and cube root functions

Graph parabolas in all forms

Graph from linear standard form

Horizontal & vertical lines

Intercepts from a table

Graphing exponential growth & decay

Intercepts from a graph

Midline of sinusoidal functions from equation

Amplitude of sinusoidal functions from graph

Piecewise functions graphs

Graph sinusoidal functions

Period of sinusoidal functions from graph

Period of sinusoidal functions from equation

End behavior of polynomials

Graphs of rational functions

Absolute maxima and minima

Evaluate step functions

Graph quadratics in factored form

274 questions14 skills

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Slope from two points

Slope from equation

Slope-intercept intro

Graph from slope-intercept form

Graph quadratics in vertex form

Intercepts from an equation

Graphing linear relationships word problems

Graph quadratics in standard form

Graph parabolas in all forms

Graph from linear standard form

Horizontal & vertical lines

Intercepts from a table

Intercepts from a graph

Graph quadratics in factored form

92 questions6 skills

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

47 questions3 skills

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

92 questions4 skills

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

225 questions11 skills

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Graphs of exponential functions

Graphs of logarithmic functions

Amplitude of sinusoidal functions from equation

Midline of sinusoidal functions from graph

Graph sinusoidal functions: phase shift

Graphing exponential growth & decay

Midline of sinusoidal functions from equation

Amplitude of sinusoidal functions from graph

Graph sinusoidal functions

Period of sinusoidal functions from graph

Period of sinusoidal functions from equation

679 questions30 skills

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Features of quadratic functions

Solve equations using structure

Completing the square (intro)

Quadratics by factoring

Slope from equation

Difference of squares intro

Completing the square

Difference of squares

Zeros of polynomials (factored form)

Perfect squares

Features of quadratic functions: strategy

Quadratic word problems (standard form)

Factor polynomials: common factor

Factor polynomials: quadratic methods

Equivalent forms of exponential expressions

Factoring quadratics intro

Factor monomials

Rewrite exponential expressions

Interpret change in exponential models: changing units

Interpret change in exponential models: with manipulation

Zeros of polynomials (with factoring)

Factor polynomials: quadratic methods (challenge)

Interpret time in exponential models

Quadratics by factoring (intro)

Factor polynomials using structure

Factor quadratics by grouping

Convert linear equations to standard form

Completing the square (intermediate)

Interpret change in exponential models

Compare features of functions

289 questions10 skills

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Features of quadratic functions

Solve equations using structure

Completing the square (intro)

Quadratics by factoring

Completing the square

Features of quadratic functions: strategy

Quadratic word problems (standard form)

Quadratics by factoring (intro)

Completing the square (intermediate)

Compare features of functions

129 questions6 skills

Use the properties of exponents to interpret expressions for exponential functions.

101 questions4 skills

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).