NJSLA Algebra I Building Functions Practice

Building Functions skills

F-BF.A.1 Write a function that describes a relationship between two quantities

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context

F-BF.A.1b Combine standard function types using arithmetic operations

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and similar transformations

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playmedium

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

Work from the outside in. Since $a(5) = 4$ , we need $b(c(x)) = 5$ . Since $b(3) = 5$ , we need $c(x) = 3$ . From the table, $c(2) = 3$ , so $x = 2$ .

Practice playmedium

$f$ and $g$ are piecewise functions.
$f(x)=\begin{cases} 5-x & \text{for } x \leq 4 \\ 2x & \text{for } x > 4 \end{cases}$
$g(x)=\begin{cases} x+6 & \text{for } x \leq 0 \\ 3x & \text{for } x > 0 \end{cases}$
Evaluate $f(g(0))\textsf{.}$

Start with the inner function: $0 \leq 0$ , so $g(0)=0+6=6$ . Then $6 > 4$ , so $f(6)=2(6)=12\textsf{.}$

Practice playeasy

The first five terms of an arithmetic sequence are $12, 18, 24, 30, 36$ . What is the $11$ th term?

The common difference is $d = 6$ . With $a_1 = 12$ , the $11$ th term is $a_{11} = 12 + 10(6) = 72$ .

Practice playeasy

Which of the following describes the transformation from the graph of $f(x)$ to the graph of $y = \dfrac{1}{3}f(x)$ ?

Multiplying every output by $\dfrac{1}{3}$ pulls the graph toward the $x$ -axis, so it is compressed vertically by a factor of $\dfrac{1}{3}$ .

Practice playeasy

How does the graph of $y = f(x)$ move as a result of the transformation $y = f(x + 4) - 2$ ?

To shift left, $x$ gets smaller but the height stays the same, so $4$ is added inside $f$ . Subtracting $2$ outside $f$ is a separate move down.

Practice playeasy

The first term of a sequence is $2$ . Each term after the first is $4$ 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 $n = 1\textsf{:}$ $2 \cdot 4^{0}$
2nd term, or $n = 2\textsf{:}$ $2 \cdot 4^{1}$
3rd term, or $n = 3\textsf{:}$ $2 \cdot 4^{2}$
4th term, or $n = 4\textsf{:}$ $2 \cdot 4^{3}$
Since each term has an exponent that is $1$ less than the term number, the $n$ th term is $a_n = 2 \cdot 4^{n-1}$ .

Practice playmedium

The graph of $2x + 4y = 8$ is translated right $2$ units on the coordinate plane. What is the $y$ -coordinate of the $y$ -intercept of the resulting graph?

A right shift of $2$ replaces $x$ with $x - 2$ . At the $y$ -intercept, $x = 0$ , so $2(-2) + 4y = 8$ . Then $-4 + 4y = 8$ , $4y = 12$ , and $y = 3$ .

Practice playeasy

Find the $4$ th term: $a_1 = 10$ , $d = -2$ .

$a_{4} = 10 + 3(-2) = 4$ .

NJSLA Algebra I Building Functions. Practice it free.

Building Functions skills

F-BF.A.1 Write a function that describes a relationship between two quantities

F-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context

F-BF.A.1b Combine standard function types using arithmetic operations

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula

F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and similar transformations

Topics mapped to this domain

Function table composition (ACT)

Piecewise function composition (ACT)

Arithmetic sequence nth term

Function transformation descriptions

Function transformations

Geometric sequence equations

Linear graph translations

Sequences and series

8 free questions · 0/0 correct

Turn building functions into game time.

More Algebra I domains