SOL Algebra II Functions and Relations Practice

Functions and Relations skills

linear, quadratic, exponential, and logarithmic functions

inverse functions

function transformations

composition and notation

Standards basis

Virginia Mathematics Standards of Learning — Virginia

How the SOL reports it

Virginia SOL math is a state-specific assessment program built around the Virginia Mathematics Standards of Learning rather than a shared national test framework. It is aligned to Virginia grade-level and course standards, which are generally CCSS-like in organization but are published as Virginia-specific standards.

Blueprint & weighting

SOL uses the Independent / state-specific framework (by grade domains structure).

Official sources

Virginia Department of Education
VDOE — Standards of Learning for Mathematics (2023 SOL grade/course standards and assessment blueprints)
VDOE — SOL Test Blueprints (per-reporting-category item counts live inside the individual grade/EOC blueprint PDFs)

8 free questions · 0/0 correct

Practice playeasy

For which value of $x$ does the graph of $y = (x - 15)(x + 7)$ intercept the $x$ -axis?

Set $y = 0$ : $(x - 15)(x + 7) = 0$ . The zeros are $x = 15$ and $x = -7$ . Of the choices, $15$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = (x - 9)^2 - 2$

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 $a = 1 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Here $h = 9$ , so the vertex is at $x = 9$ . Therefore, $f(x)$ reaches its minimum when $x = 9$ .

Practice playeasy

The equation $y = x^2 + 4x + 3$ models a quantity $y$ in terms of $x$ . For what value of $x$ is $y$ as small as possible?

The parabola opens upward, so the smallest $y$ is at 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, $y$ is as small as possible when $x = -2$ .

Practice playeasy

The function $f$ is defined by $f(x) = \sqrt{x + 21}$ . What is the value of $f(x)$ when $x = 4$ ?

Substitute $x = 4$ : $f(4) = \sqrt{4 + 21} = \sqrt{25} = 5$ .

Practice playeasy

The function $f$ is defined by $f(x) = -2x + 15$ . What is the value of $f(x)$ when $x = 3$ ?

Substitute $x = 3$ : $f(3) = -2(3) + 15 = -6 + 15 = 9$ .

Practice playeasy

For the function $g$ , $g(0) = 100$ . For each increase in $x$ by $1$ , the value of $g(x)$ increases by $50\%$ . What is the value of $g(2)$ ?

Each step multiplies by $1 + 0.50 = 1.5$ . So $g(2) = 100 \cdot 1.5^2 = 100 \cdot 2.25 = 225$ .

Practice playeasy

$r = 120 - 8s$

The equation shown gives the estimated number of raffle tickets $r$ remaining after $s$ sales periods at a festival booth, where $0 \le s \le 15\textsf{.}$ What is the estimated number of raffle tickets remaining after $7$ sales periods?

Substitute $s = 7\textsf{:}$ $r = 120 - 8(7) = 120 - 56 = 64\textsf{.}$ The estimated number remaining is $64\textsf{.}$

Practice playmedium

The function $P$ is defined by $P(x) = -2x^{2} + 40x - 50$ . The function models the profit, in dollars, from selling $x$ handmade notebooks at a school fair. The domain of the function is $0 \le x \le 20$ . Which of the following is the best interpretation of the statement " $P(5)$ is equal to $100$ " in this context?

Here $x$ is the number of notebooks sold and $P(x)$ is profit in dollars. So $P(5) = 100$ means that when $5$ notebooks are sold, the profit is $100$ dollars.

SOL Algebra II Functions and Relations. Practice it free.

Functions and Relations skills

linear, quadratic, exponential, and logarithmic functions

inverse functions

function transformations

composition and notation

Topics mapped to this domain

Factored polynomial x-intercepts (SAT)

Quadratic minimum from vertex form

Quadratic minimum x-value

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Interpreting function values in context

Logarithm rules

Quadratic function word problems (ACT)

Finding inverse functions (ACT)

Function transformation descriptions

8 free questions · 0/0 correct

Turn functions and relations into game time.

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