NY State Math Algebra I Functions Practice

NY State Math Algebra I Functions. Practice it free.

Per the NYSED Algebra I Educator Guide blueprint, the Functions conceptual category is 24%–32% of credit and includes the domains Interpreting Functions (F-IF), Building Functions (F-BF), and Linear, Quadratic, and Exponential Models (F-LE). This Algebra I reporting domain maps to 31 practice skills and 8 representative questions from the playable bank.

Algebra IF-IF, F-BF, F-LE31 mapped skills

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

Build new functions from existing functions

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Standards basis

New York State Learning Standards / New York State Next Generation Learning Standards (NGLS) — New York

How the NY State Math reports it

New York’s Grades 3–8 math tests and Regents math exams are state-developed assessments rather than a shared national framework. The grades 3–8 exams are aligned to New York State learning standards, and the Regents math sequence includes Algebra I, Geometry, and Algebra II, with the June 2026 Algebra II exam explicitly based on the New York State Next Generation Learning Standards.

Blueprint & weighting

Grades 3–8: the official page and the retrieved administration guide describe item/credit structure and timing, but no published domain-by-domain blueprint weighting was located in the primary sources used here. Regents (high school): NYSED publishes a per-conceptual-category 'percent of test by credit' blueprint for each course in its Educator Guides. Algebra I — Number & Quantity 4%–10%, Algebra 48%–61%, Functions 24%–32%, Statistics & Probability 7%–15%. Geometry (single conceptual category, by domain) — Congruence (G-CO) 27%–34%, Similarity, Right Triangles, & Trigonometry (G-SRT) 29%–37%, Circles (G-C) 2%–8%, Expressing Geometric Properties with Equations (G-GPE) 12%–18%, Geometric Measurement & Dimensions (G-GMD) 2%–8%, Modeling with Geometry (G-MG) 8%–15%. Algebra II — Number & Quantity 4%–8%, Algebra 30%–39%, Functions 38%–45%, Statistics & Probability 14%–22%.

Official sources

NYSED Grades 3–8 ELA and Math Test Manuals
NYSED Directions for Administering Regents Examinations
NYSED High School Regents Examinations

8 free questions · 0/0 correct

Practice playeasy

At what $x$ -value does the graph of $y = 4(x + 12)(x - 3)(x + 2)$ intercept the $x$ -axis?

Set $y = 0$ : $4(x + 12)(x - 3)(x + 2) = 0$ . The constant $4 \neq 0$ , so the zeros are $x = -12$ , $x = 3$ , and $x = -2$ . Among the choices, only $3$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = 3(x - 1)^2 + 7$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

The equation is in vertex form $f(x) = a(x - h)^2 + k$ with $a = 3 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 1$ , so the vertex is at $x = 1$ . The leading coefficient $3$ does not change the $x$ -coordinate of the vertex. Therefore, $f(x)$ reaches its minimum when $x = 1$ .

Practice playeasy

The graph of $y = x^2 - 4x + 1$ is a parabola that opens upward. What is the $x$ -coordinate of its lowest point?

Because this parabola opens upward, its lowest point is the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 1$ and $b = -4$ , so $x = -\dfrac{-4}{2(1)} = \dfrac{4}{2} = 2$ . Therefore, the lowest point has $x$ -coordinate $2$ .

Practice playmedium

A lab culture starts with $2{,}000$ cells. Each hour, a model estimates that the number of cells triples. Which equation defines this model, where $c(h)$ is the estimated number of cells $h$ hours after the culture begins?

The starting count is $2{,}000$ , and tripling each hour means multiplying by $3$ , so $c(h) = 2{,}000(3)^h$ .

Practice playeasy

The function $p$ is defined by $p(w) = 1{,}250(1.04)^{w}$ . The function models a savings balance, in dollars, $w$ weeks after an account is opened. Which statement is the best interpretation of $1{,}250$ in this context?

When $w = 0$ , $p(0) = 1{,}250$ . So $\text{\char36}1{,}250$ is the balance when the account is opened.

Practice playeasy

A plant's height $H$ , in centimeters, after $w$ weeks of growth is modeled by $H = 1.8w + 12$ . Which of the following is the best interpretation of $1.8$ in this context?

In $H = 1.8w + 12$ , the $1.8$ multiplies weeks, so the plant grows $1.8$ centimeters each week.

Practice playeasy

A plumber charges a flat fee for a service visit plus a fixed amount per hour of work. Let $h$ be the number of hours worked and $C$ be the total charge in dollars. The situation is modeled by $C = 65h + 40$ . Which is the best interpretation of the number $65$ in this equation?

The coefficient of $h$ is the hourly rate, so $65$ is the charge in dollars for each hour of work.

Practice playmedium

The first five terms of an arithmetic sequence are $5, 9, 13, 17, 21$ . What is the $20$ th term?

The common difference is $d = 4$ . With $a_1 = 5$ , the $20$ th term is $a_{20} = 5 + 19(4) = 81$ .

NY State Math Algebra I Functions. Practice it free.

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

Build new functions from existing functions

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Topics mapped to this domain

Factored polynomial x-intercepts (SAT)

Quadratic minimum from vertex form

Quadratic minimum x-value

Writing exponential equations from context (SAT)

Interpreting exponential parameters

Interpreting linear parameters

Linear coefficient interpretations (SAT/PSAT 8/9/10)

Arithmetic sequence nth term

Finding inverse functions (ACT)

Function table composition (ACT)

Function transformation descriptions

Function transformations

8 free questions · 0/0 correct

Turn functions into game time.

More Algebra I domains