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- Common Core MathK - 8High School

# Functions: Interpreting Functions

2003 questions102 skills

# Functions: Interpreting Functions

2003 questions102 skills

## HSF-IF.A.1

227 questions11 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*).Domain of advanced functions

Evaluate function expressions

Range of quadratic functions

Evaluate functions from their graph

Function rules from equations

Function inputs & outputs: graph

Identifying values in the domain

Function inputs & outputs: equation

Domain of advanced piecewise functions

Recognize functions from tables

Recognize functions from graphs

## HSF-IF.A.2

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.

Use arithmetic sequence formulas

Use geometric sequence formulas

Evaluate functions

Evaluate function expressions

Evaluate functions from their graph

Evaluate step functions

Function inputs & outputs: graph

Evaluate sequences in recursive form

Function notation word problems

Function inputs & outputs: equation

Evaluate piecewise functions

## HSF-IF.A.3

114 questions6 skills

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

## HSF-IF.B.4

278 questions15 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*.Using slope and intercepts in context

Quadratic word problems (standard form)

Linear equations word problems: tables

Periodicity of algebraic models

Graph interpretation word problems

Comparing linear functions word problems

Interpret parabolas in context

End behavior of algebraic models

Interpret a quadratic graph

Linear models word problems

Relating linear contexts to graph features

Linear equations word problems: graphs

Quadratic word problems (vertex form)

Quadratic word problems (factored form)

Connecting exponential graphs with contexts

## HSF-IF.B.5

46 questions3 skills

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

## HSF-IF.B.6

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.

## HSF-IF.C.7

533 questions29 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 and negative intervals

Graph sinusoidal functions

Intercepts from an equation

Graph quadratics in vertex form

Graph parabolas in all forms

Graph quadratics in standard form

Graphs of logarithmic functions

Graphing from slope

Slope-intercept intro

Graph sinusoidal functions: phase shift

Intercepts from a graph

Slope from two points

Graph from linear standard form

Intercepts from a table

Evaluate step functions

Increasing and decreasing intervals

Horizontal & vertical lines

Graphing exponential growth & decay

Graph from slope-intercept form

Graph absolute value functions

Absolute maxima and minima

Graphs of exponential growth

Piecewise functions graphs

Relative maxima and minima

Graphing linear relationships word problems

Slope from equation

Graphs of nonlinear piecewise functions

Graph quadratics in factored form

Evaluate piecewise functions

## HSF-IF.C.7a

305 questions17 skills

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

Intercepts from an equation

Graph quadratics in vertex form

Graph parabolas in all forms

Graph quadratics in standard form

Slope-intercept intro

Intercepts from a graph

Slope from two points

Graph from linear standard form

Intercepts from a table

Horizontal & vertical lines

Graph from slope-intercept form

Interpret parabolas in context

Interpret a quadratic graph

Graphing linear relationships word problems

Slope from equation

Graph quadratics in factored form

Parabolas intro

## HSF-IF.C.7b

92 questions6 skills

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

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

Skills for this standard are coming soon.

## HSF-IF.C.7d

20 questions1 skill

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

## HSF-IF.C.7e

135 questions7 skills

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

## HSF-IF.C.8

565 questions26 skills

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

Parallel & perpendicular lines from equation

Quadratics by factoring (intro)

Convert linear equations to standard form

Completing the square (intermediate)

Completing the square

Difference of squares

Factoring quadratics intro

Difference of squares intro

Quadratics by factoring

Factor polynomials: quadratic methods

Factor polynomials: quadratic methods (challenge)

Factor quadratics by grouping

Quadratic word problems (standard form)

Zeros of polynomials (with factoring)

Interpret quadratic models

Solve equations using structure

Completing the square (intro)

Features of quadratic functions

Slope from equation

Features of quadratic functions: strategy

Interpret change in exponential models: changing units

Perfect squares intro

Compare features of functions

Interpret change in exponential models: with manipulation

Factoring quadratics with a common factor

Perfect squares

## HSF-IF.C.8a

317 questions12 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.

Quadratics by factoring (intro)

Completing the square (intermediate)

Completing the square

Quadratics by factoring

Quadratic word problems (standard form)

Interpret quadratic models

Solve equations using structure

Completing the square (intro)

Features of quadratic functions

Features of quadratic functions: strategy

Compare features of functions

Zero product property

## HSF-IF.C.8b

35 questions2 skills

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

## HSF-IF.C.9

101 questions4 skills

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