Georgia Milestones 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

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

Official sources

Georgia Department of Education

8 free questions · 0/0 correct

Practice playeasy

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

Substitute $x = 4$ : $f(4) = 3 \cdot 2^{4} = 3 \cdot 16 = 48$ .

Practice playeasy

The function $f$ is defined by $f(x) = 5x - 7$ . What is the value of $f(x)$ when $x = 2$ ?

Substitute $x = 2$ : $f(2) = 5(2) - 7 = 10 - 7 = 3$ .

Practice playmedium

For the function $q$ , $q(0) = 500$ . For each increase in $x$ by $1$ , the value of $q(x)$ decreases by $20\%$ . What is the value of $q(3)$ ?

Each step multiplies by $0.80$ . So $q(3) = 500 \cdot 0.80^3 = 500 \cdot 0.512 = 256$ .

Practice playeasy

$p = 320 - 40d$

The equation shown gives the estimated number of pages $p$ left to read in a book after $d$ days of a reading plan, where $0 \le d \le 8\textsf{.}$ What is the estimated number of pages left to read after $5$ days of the reading plan?

Substitute $d = 5\textsf{:}$ $p = 320 - 40(5) = 320 - 200 = 120\textsf{.}$ The estimated number of pages left is $120\textsf{.}$

Practice playeasy

The graph of $f(x) = 2(x - 6)(x - 1)(x + 10)$ meets the $x$ -axis at which value of $x$ ?

Set $f(x) = 0$ : $2(x - 6)(x - 1)(x + 10) = 0$ . The constant $2 \neq 0$ , so the zeros are $x = 6$ , $x = 1$ , and $x = -10$ . Among the choices, only $-10$ is an x-coordinate of an x-intercept.

Practice playmedium

The function $W$ is defined by $W(t) = 40t + 120$ . The function models the number of gallons of water in a tank $t$ minutes after filling begins. Which of the following is the best interpretation of the statement " $W(5)$ is equal to $320$ " in this context?

Here $t$ is minutes after filling begins and $W(t)$ is gallons in the tank. So $W(5) = 320$ means that $5$ minutes after filling begins, the tank holds $320$ gallons.

Practice playmedium

A parabolic bridge arch has height $h$ , in meters, at a horizontal distance $x$ meters from the left pillar modeled by $h(x) = -x^2 + 10x + 15$ . According to the model, what is the height, in meters, of the arch $8$ meters from the left pillar?

Substitute $x = 8$ : $h(8) = -(8^2) + 10(8) + 15 = -64 + 80 + 15 = 31$ meters.

Practice playeasy

$f(x) = (x - 5)^2 + 11$

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 $h = 5$ , so the vertex is at $x = 5$ . Therefore, $f(x)$ reaches its minimum when $x = 5$ .

Georgia Milestones 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

Topics mapped to this domain

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)

Quadratic minimum from vertex form

Quadratic minimum x-value

Recursive sequence nth term (ACT)

Slope-intercept intercepts (SAT/PSAT 8/9/10)

8 free questions · 0/0 correct

Turn interpreting functions into game time.

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