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- Common Core MathK - 8High School

# Functions: Building Functions

967 questions49 skills

# Functions: Building Functions

967 questions49 skills

## HSF-BF.A.1

178 questions9 skills

Write a function that describes a relationship between two quantities.

## HSF-BF.A.1a

84 questions5 skills

Determine an explicit expression, a recursive process, or steps for calculation from a context.

## HSF-BF.A.1b

16 questions1 skill

Combine standard function types using arithmetic operations.

## HSF-BF.A.1c

88 questions4 skills

Compose functions.

## HSF-BF.A.2

130 questions7 skills

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Recursive formulas for arithmetic sequences

Converting recursive & explicit forms of arithmetic sequences

Recursive formulas for geometric sequences

Explicit formulas for geometric sequences

Converting recursive & explicit forms of geometric sequences

Sequences word problems

Explicit formulas for arithmetic sequences

## HSF-BF.B.3

385 questions19 skills

Identify the effect on the graph of replacing

*f*(*x*) by*f*(*x*) +*k*,*k**f*(*x*),*f*(*kx*), and*f*(*x*+*k*) for specific values of*k*(both positive and negative); find the value of*k*given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.Graph sinusoidal functions

Even and odd functions: Graphs and tables

Identify function transformations

Graphs of logarithmic functions

Scale functions horizontally

Amplitude of sinusoidal functions from equation

Graph sinusoidal functions: phase shift

Scale & reflect absolute value graphs

Period of sinusoidal functions from equation

Graphs of square and cube root functions

Reflect functions

Graphs of exponential functions

Shift functions

Scale functions vertically

Scale & reflect parabolas

Even & odd functions: Equations

Shift absolute value graphs

Midline of sinusoidal functions from equation

Shift parabolas

## HSF-BF.B.4

109 questions7 skills

Find inverse functions.

## HSF-BF.B.4a

24 questions2 skills

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

## HSF-BF.B.4b

16 questions1 skill

Verify by composition that one function is the inverse of another.

## HSF-BF.B.4c

38 questions2 skills

Read values of an inverse function from a graph or a table, given that the function has an inverse.

## HSF-BF.B.4d

31 questions2 skills

Produce an invertible function from a non-invertible function by restricting the domain.

## HSF-BF.B.5

115 questions4 skills

Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.