DC CAPE 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

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

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

The $x$ -intercept of the graph of $y = -4x - 20$ in the coordinate plane is $(x, 0)$ . What is the value of $x$ ?

At the $x$ -intercept, $y = 0$ , so $0 = -4x - 20$ , $-4x = 20$ , and $x = -5\textsf{.}$

Practice playeasy

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

Substitute $x = 2$ : $f(2) = 3(2)^{2} + 2 = 3(4) + 2 = 12 + 2 = 14$ .

Practice playeasy

The function $f(x)$ is defined by $f(x) = -3x + 20$ . For what value of $x$ does $f(x) = 5$ ?

Set $-3x + 20 = 5$ . Then $-3x = -15$ , so $x = 5$ .

Practice playeasy

For the function $h$ , $h(0) = 64$ . For each increase in $x$ by $1$ , the value of $h(x)$ decreases by $25\%$ . What is the value of $h(2)$ ?

Each step multiplies by $1 - 0.25 = 0.75$ . So $h(2) = 64 \cdot 0.75^2 = 64 \cdot 0.5625 = 36$ .

Practice playeasy

$a = 250 + 15w$

The equation shown gives the estimated balance $a\textsf{,}$ in dollars, in a savings account after $w$ weeks of deposits, where $0 \le w \le 20\textsf{.}$ What is the estimated balance, in dollars, in the savings account after $6$ weeks of deposits?

Substitute $w = 6\textsf{:}$ $a = 250 + 15(6) = 250 + 90 = 340\textsf{.}$ The estimated balance is $340$ dollars.

DC CAPE 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

Factored polynomial x-intercepts (SAT)

Quadratic minimum from vertex form

Quadratic minimum x-value

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

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Interpreting function values in context

Quadratic function word problems (ACT)

Recursive sequence nth term (ACT)

8 free questions · 0/0 correct

Turn interpreting functions into game time.

More Algebra I domains