Georgia Milestones Algebra I 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 $f(x) = x^{2} - 10$ . What is the value of $f(x)$ when $x = 6$ ?

Substitute $x = 6$ : $f(6) = 6^{2} - 10 = 36 - 10 = 26$ .

Practice playeasy

The function $f$ is defined by $f(x) = \sqrt{x + 5}$ . What is the value of $f(x)$ when $x = 11$ ?

Substitute $x = 11$ : $f(11) = \sqrt{11 + 5} = \sqrt{16} = 4$ .

Practice playeasy

For the function $f$ , $f(0) = 160$ . For each increase in $x$ by $1$ , the value of $f(x)$ decreases by $50\%$ . What is the value of $f(3)$ ?

A decrease of $50\%$ multiplies by $0.50$ each step. So $f(3) = 160 \cdot 0.50^3 = 160 \cdot 0.125 = 20$ .

Practice playeasy

$b = 100 - 4h$

The equation shown gives the estimated battery charge $b\textsf{,}$ as a percent, remaining on a laptop after $h$ hours of use, where $0 \le h \le 20\textsf{.}$ What is the estimated battery charge, as a percent, remaining on the laptop after $12$ hours of use?

Substitute $h = 12\textsf{:}$ $b = 100 - 4(12) = 100 - 48 = 52\textsf{.}$ The estimated charge remaining is $52$ percent.

Practice playeasy

For which value of $x$ does the graph of $y = -(x + 8)(x - 2)$ meet the $x$ -axis?

Set $y = 0$ : $-(x + 8)(x - 2) = 0$ . The factor $-1$ is nonzero, so the zeros come from $x + 8 = 0 \Rightarrow x = -8$ and $x - 2 = 0 \Rightarrow x = 2$ . Of the choices, $-8$ is an x-coordinate of an x-intercept.

Practice playmedium

The function $T$ is defined by $T(d) = -4d + 86$ . The function models the outdoor temperature, in degrees Fahrenheit, $d$ days after a cold front arrives. The domain of the function is $0 \le d \le 10$ . Which of the following is the best interpretation of the statement " $T(3)$ is equal to $74$ " in this context?

In this model, $d$ is days after the cold front arrives and $T(d)$ is the temperature in degrees Fahrenheit. So $T(3) = 74$ means that $3$ days after the cold front arrives, the temperature is $74$ degrees Fahrenheit.

Practice playmedium

A town's population $P$ , in thousands, $t$ years after a census is modeled by $P(t) = -t^2 + 14t + 120$ . According to the model, what is the population, in thousands, $6$ years after the census?

Substitute $t = 6$ : $P(6) = -(6^2) + 14(6) + 120 = -36 + 84 + 120 = 168$ thousand.

Practice playeasy

$f(x) = 4(x + 1)^2 - 3$

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 $a = 4 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Rewrite $(x + 1)^2$ as $(x - (-1))^2$ : the vertex is at $x = -1$ . The leading coefficient $4$ does not change the $x$ -coordinate of the vertex. Therefore, $f(x)$ reaches its minimum when $x = -1$ .

Georgia Milestones Algebra I 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.

More Algebra I domains