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### Math

## Common Core Math

# High School: Functions: Interpreting Functions

### HSF.IF.A.1

Fully covered

- Determining whether values are in domain of function
- Does a vertical line represent a function?
- Domain of advanced functions
- Domain of advanced piecewise functions
- Equations vs. functions
- Evaluate function expressions
- Evaluate functions from their graph
- Evaluating discrete functions
- Function inputs & outputs: equation
- Function inputs & outputs: graph
- Function rules from equations
- Identifying values in the domain
- Obtaining a function from an equation
- Range of quadratic functions
- Recognize functions from graphs
- Recognize functions from tables
- Recognizing functions from graph
- Recognizing functions from table
- Recognizing functions from verbal description
- Recognizing functions from verbal description word problems
- What is a function?
- What is the domain of a function?
- What is the range of a function?
- Worked example: domain & range of piecewise linear functions
- Worked example: domain & range of step function
- Worked example: evaluating expressions with function notation
- Worked example: Evaluating functions from graph
- Worked example: matching an input to a function's output (equation)
- Worked example: matching an input to a function's output (graph)
- Worked example: two inputs with the same output (graph)

### HSF.IF.A.2

Fully covered

- Evaluate function expressions
- Evaluate functions
- Evaluate functions from their graph
- Evaluate piecewise functions
- Evaluate sequences in recursive form
- Evaluate step functions
- Evaluating discrete functions
- Evaluating polynomials
- Evaluating sequences in recursive form
- Function inputs & outputs: equation
- Function inputs & outputs: graph
- Function notation word problem: bank
- Function notation word problem: beach
- Function notation word problems
- Geometric sequences review
- Intro to arithmetic sequence formulas
- Use arithmetic sequence formulas
- Use geometric sequence formulas
- Using arithmetic sequences formulas
- Using explicit formulas of geometric sequences
- Using recursive formulas of geometric sequences
- What is a function?
- Worked example: evaluating expressions with function notation
- Worked example: Evaluating functions from equation
- Worked example: Evaluating functions from graph
- Worked example: evaluating piecewise functions
- Worked example: matching an input to a function's output (equation)
- Worked example: matching an input to a function's output (graph)
- Worked example: two inputs with the same output (graph)
- Worked example: using recursive formula for arithmetic sequence

### HSF.IF.A.3

Mostly covered

- Arithmetic sequences review
- Extend arithmetic sequences
- Extend geometric sequences
- Extend geometric sequences: negatives & fractions
- Extending arithmetic sequences
- Extending geometric sequences
- Geometric sequences review
- Intro to arithmetic sequence formulas
- Intro to arithmetic sequences
- Intro to arithmetic sequences
- Intro to geometric sequences
- Sequences and domain
- Sequences and domain
- Sequences intro
- Use arithmetic sequence formulas
- Use geometric sequence formulas
- Using arithmetic sequences formulas
- Using explicit formulas of geometric sequences
- Using recursive formulas of geometric sequences
- Worked example: using recursive formula for arithmetic sequence

### HSF.IF.B.4

Partially covered

- Analyzing graphs of exponential functions
- Analyzing graphs of exponential functions: negative initial value
- Analyzing tables of exponential functions
- Comparing linear functions word problem: climb
- Comparing linear functions word problem: walk
- Comparing linear functions word problem: work
- Comparing linear functions word problems
- Connecting exponential graphs with contexts
- End behavior of algebraic models
- End behavior of algebraic models
- Finding slope and intercepts from tables
- Graph interpretation word problem: basketball
- Graph interpretation word problem: temperature
- Graph interpretation word problems
- Interpret a quadratic graph
- Interpret a quadratic graph
- Interpret parabolas in context
- Linear equations word problems: earnings
- Linear equations word problems: graphs
- Linear equations word problems: tables
- Linear equations word problems: volcano
- Linear graphs word problem: cats
- Linear graphs word problems
- Linear models word problem: book
- Linear models word problem: marbles
- Linear models word problems
- Modeling with linear equations: snow
- Periodicity of algebraic models
- Periodicity of algebraic models
- Quadratic word problem: ball
- Quadratic word problem: mosquitoes
- Quadratic word problems (factored form)
- Quadratic word problems (factored form)
- Quadratic word problems (standard form)
- Quadratic word problems (vertex form)
- Quadratic word problems (vertex form)
- Relating linear contexts to graph features
- Slope and intercept meaning from a table
- Slope and intercept meaning in context
- Slope, x-intercept, y-intercept meaning in context
- Symmetry of algebraic models
- Symmetry of algebraic models
- Using slope and intercepts in context

### HSF.IF.B.5

Fully covered

- Determine the domain of functions
- Domain and range from graph
- Domain of a radical function
- Examples finding the domain of functions
- Function domain word problems
- Modeling with linear equations: snow
- Worked example: determining domain word problem (all integers)
- Worked example: determining domain word problem (positive integers)
- Worked example: determining domain word problem (real numbers)
- Worked example: domain and range from graph
- Worked example: domain of algebraic functions

### HSF.IF.B.6

Fully covered

- Average rate of change of polynomials
- Average rate of change review
- Average rate of change word problem: equation
- Average rate of change word problem: graph
- Average rate of change word problem: table
- Average rate of change word problems
- Average rate of change: graphs & tables
- Finding average rate of change of polynomials
- Introduction to average rate of change
- Sign of average rate of change of polynomials
- Worked example: average rate of change from equation
- Worked example: average rate of change from graph
- Worked example: average rate of change from table

#### HSF.IF.C.7.a

Partially covered

- Finding features of quadratic functions
- Finding the vertex of a parabola in standard form
- Graph from linear standard form
- Graph from slope-intercept equation
- Graph from slope-intercept form
- Graph parabolas in all forms
- Graph quadratics in factored form
- Graph quadratics in standard form
- Graph quadratics in vertex form
- Graphing a linear equation: 5x+2y=20
- Graphing linear relationships word problems
- Graphing lines from slope-intercept form review
- Graphing parabolas intro
- Graphing quadratics in factored form
- Graphing quadratics review
- Graphing quadratics: standard form
- Graphing quadratics: vertex form
- Graphing slope-intercept form
- Horizontal & vertical lines
- Horizontal & vertical lines
- Intercepts from a graph
- Intercepts from a table
- Intercepts from a table
- Intercepts from an equation
- Intercepts from an equation
- Intercepts of lines review (x-intercepts and y-intercepts)
- Interpret a quadratic graph
- Interpret a quadratic graph
- Interpret parabolas in context
- Interpreting a parabola in context
- Intro to intercepts
- Intro to linear equation standard form
- Intro to point-slope form
- Intro to slope
- Intro to slope-intercept form
- Intro to slope-intercept form
- Linear functions word problem: fuel
- Linear functions word problem: pool
- Parabolas intro
- Parabolas intro
- Point-slope & slope-intercept equations
- Positive & negative slope
- Quadratic word problems (factored form)
- Quadratic word problems (vertex form)
- Slope from equation
- Slope from two points
- Slope of a horizontal line
- Slope review
- Slope-intercept intro
- Standard form review
- Vertex form introduction
- Worked example: slope from two points
- x-intercept of a line

#### HSF.IF.C.7.b

Mostly covered

- Absolute value graphs review
- Evaluate piecewise functions
- Evaluate step functions
- Graph absolute value functions
- Graphing absolute value functions
- Graphing square and cube root functions
- Graphs of nonlinear piecewise functions
- Graphs of square and cube root functions
- Graphs of square-root functions
- Introduction to piecewise functions
- Piecewise functions graphs
- Radical functions & their graphs
- Square-root functions & their graphs
- Transforming the square-root function
- Worked example: evaluating piecewise functions
- Worked example: graphing piecewise functions

#### HSF.IF.C.7.c

Fully covered

#### HSF.IF.C.7.d

Fully covered

- Graphing rational functions 1
- Graphing rational functions 2
- Graphing rational functions 3
- Graphing rational functions 4
- Graphing rational functions according to asymptotes
- Graphs of rational functions
- Graphs of rational functions (old example)
- Graphs of rational functions: horizontal asymptote
- Graphs of rational functions: vertical asymptotes
- Graphs of rational functions: y-intercept
- Graphs of rational functions: zeros

#### HSF.IF.C.7.e

Mostly covered

- Example: Graphing y=-cos(π⋅x)+1.5
- Example: Graphing y=3⋅sin(½⋅x)-2
- Exponential function graph
- Graph sinusoidal functions
- Graph sinusoidal functions: phase shift
- Graphing exponential functions
- Graphing exponential growth & decay
- Graphing exponential growth & decay
- Graphing logarithmic functions (example 1)
- Graphing logarithmic functions (example 2)
- Graphs of exponential functions
- Graphs of exponential functions (old example)
- Graphs of exponential growth
- Graphs of exponential growth
- Graphs of logarithmic functions
- Graphs of logarithmic functions
- Interpreting trigonometric graphs in context
- Intro to exponential functions
- Transforming exponential graphs
- Transforming exponential graphs (example 2)

#### HSF.IF.C.8.a

Fully covered

- Compare features of functions
- Comparing features of quadratic functions
- Comparing functions: shared features
- Comparing maximum points of quadratic functions
- Completing the square
- Completing the square (intermediate)
- Completing the square (intro)
- Completing the square review
- Features of quadratic functions
- Features of quadratic functions: strategy
- Finding features of quadratic functions
- Finding the vertex of a parabola in standard form
- Forms & features of quadratic functions
- Interpret quadratic models
- Interpret quadratic models: Factored form
- Interpret quadratic models: Vertex form
- Quadratic word problem: mosquitoes
- Quadratic word problems (standard form)
- Quadratics by factoring
- Quadratics by factoring (intro)
- Solve equations using structure
- Solving quadratics by completing the square
- Solving quadratics by factoring
- Solving quadratics by factoring
- Solving quadratics by factoring review
- Solving quadratics by factoring: leading coefficient ≠ 1
- Solving quadratics using structure
- Vertex & axis of symmetry of a parabola
- Worked example: completing the square (leading coefficient ≠ 1)
- Worked example: Rewriting & solving equations by completing the square
- Worked example: Rewriting expressions by completing the square
- Worked examples: Forms & features of quadratic functions
- Zero product property
- Zero product property

#### HSF.IF.C.8.b

Fully covered

### HSF.IF.C.9

Fully covered

- Compare features of functions
- Compare linear functions
- Compare quadratic functions
- Comparing features of quadratic functions
- Comparing functions: shared features
- Comparing functions: x-intercepts
- Comparing linear functions word problem: climb
- Comparing linear functions word problem: walk
- Comparing linear functions word problem: work
- Comparing linear functions word problems
- Comparing linear functions: equation vs. graph
- Comparing linear functions: faster rate of change
- Comparing linear functions: same rate of change
- Comparing maximum points of quadratic functions