PARCC Algebra II Interpreting Functions Practice

Interpreting Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build a function that models a relationship between two quantities

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / PARCC Model Content Frameworks — national

How the PARCC reports it

PARCC was a multistate assessment system built around the Common Core-era PARCC mathematics model content frameworks rather than a separate proprietary standards set. Its math structure is organized by grade/course and aligned to CCSS-M content categories and model content frameworks.

Blueprint & weighting

No single published PARCC weighting table was located in the accessible sources used here.

Official sources

PARCC Assessment
Common Core State Standards Initiative

8 free questions · 0/0 correct

Practice playmedium

The first five terms of an arithmetic sequence are $25, 22, 19, 16, 13$ . What is the $15$ th term?

The common difference is $d = -3$ . With $a_1 = 25$ , the $15$ th term is $a_{15} = 25 + 14(-3) = -17$ .

Practice playmedium

The table defines functions for positive integers $x \leq 5$ .
$\begin{array}{c|c|c|c} x & m(x) & n(x) & k(x) \\ \hline 1 & 5 & 2 & 4 \\ 2 & 3 & 4 & 1 \\ 3 & 1 & 3 & 5 \\ 4 & 4 & 5 & 2 \\ 5 & 2 & 1 & 3 \end{array}$
If $m(n(k(x))) = 1$ , what is the value of $x$ ?

Work from the outside in. Since $m(3) = 1$ , we need $n(k(x)) = 3$ . Since $n(3) = 3$ , we need $k(x) = 3$ . From the table, $k(5) = 3$ , so $x = 5$ .

Practice playeasy

The first term of a sequence is $10$ . Each term after the first is $2$ times the preceding term. If $a_n$ represents the $n$ th term, which equation gives $a_n$ in terms of $n$ ?

Following the pattern:
1st term, or $n = 1\textsf{:}$ $10 \cdot 2^{0}$
2nd term, or $n = 2\textsf{:}$ $10 \cdot 2^{1}$
3rd term, or $n = 3\textsf{:}$ $10 \cdot 2^{2}$
4th term, or $n = 4\textsf{:}$ $10 \cdot 2^{3}$
Since each term has an exponent that is $1$ less than the term number, the $n$ th term is $a_n = 10 \cdot 2^{n-1}$ .

Practice playhard

The piecewise functions $f$ and $g$ are given.
$f(x)=\begin{cases} 4x-1 & \text{for } x \leq -1 \\ 3-x & \text{for } x > -1 \end{cases}$
$g(x)=\begin{cases} x+8 & \text{for } x \leq 2 \\ 5x & \text{for } x > 2 \end{cases}$
$f(g(1))=$

Start with the inner function: $1 \leq 2$ , so $g(1)=1+8=9$ . Then $9 > -1$ , so $f(9)=3-9=-6\textsf{.}$

Practice playeasy

Find the sum: $1 + 3 + 9$ .

Geometric series: $1 + 3 + 9 = 13$ .

Practice playeasy

The function $f$ is defined by $f(x) = -3x + 22$ . What is the value of $f(x)$ when $x = 5$ ?

Substitute $x = 5$ : $f(5) = -3(5) + 22 = -15 + 22 = 7$ .

Practice playeasy

The function $f$ is defined by $f(x) = x^2 + 3$ . What is the value of $f(x)$ when $x = 4$ ?

Substitute $x = 4$ : $f(4) = 4^2 + 3 = 16 + 3 = 19$ .

Practice playeasy

For the function $f$ , $f(0) = 250$ . For each increase in $x$ by $1$ , the value of $f(x)$ decreases by $40\%$ . What is the value of $f(2)$ ?

Each step multiplies by $1 - 0.40 = 0.60$ . So $f(2) = 250 \cdot 0.60^2 = 250 \cdot 0.36 = 90$ .

PARCC Algebra II Interpreting Functions. Practice it free.

Interpreting Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build a function that models a relationship between two quantities

Topics mapped to this domain

Arithmetic sequence nth term

Function table composition (ACT)

Geometric sequence equations

Piecewise function composition (ACT)

Sequences and series

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Factored polynomial x-intercepts (SAT)

Interpreting function values in context

Quadratic function word problems (ACT)

8 free questions · 0/0 correct

Turn interpreting functions into game time.

More Algebra II domains