DC CAPE Algebra II Building Functions Practice

Building Functions skills

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

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

The function $I$ is defined by $I(t) = 275(1.04)^t$ . The function $I$ models the balance, in thousands of dollars, of an investment account, where $t$ is the number of months after the account was opened. According to the model, what is the estimated balance, in thousands of dollars, of the account $1$ month after it was opened?

When $t = 1$ , $I(1) = 275(1.04)^1 = 275 \cdot 1.04 = 286$ thousand dollars.

Practice playeasy

You invest $\text{\char36}400$ at $25\%$ annual interest for $1$ year. What is the total?

$400 \times 1.25 = 500$ .

Practice playmedium

Candle height, in cm, after $x$ hours:
$\begin{array}{c|c} x & f(x) \\ \hline 0 & 20 \\ 1 & 18 \\ 2 & 16 \\ 3 & 14 \end{array}$
The height is $f(x)=mx+20\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The height decreases by $2$ centimeters each hour, so $m = -2\textsf{.}$

Practice playmedium

The table shows values of a linear function $h\textsf{.}$
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline h(x) & 7 & 10 & 13 & 16 \end{array}$
Which of the following is $h(x)\textsf{?}$

The outputs increase by $3$ each time $x$ increases by $1\textsf{,}$ so the constant rate is $3\textsf{.}$ Using the point $(1, 7)$ gives $3(1) + b = 7\textsf{,}$ so $b = 4\textsf{.}$ Therefore $h(x) = 3x + 4\textsf{.}$

Practice playeasy

A line has slope $4$ and passes through the point $(-1, 2)$ . Which equation represents this line in point-slope form?

Point-slope form is $y - y_1 = m(x - x_1)$ . With $m = 4$ and $(x_1, y_1) = (-1, 2)$ , the equation is $y - 2 = 4(x - (-1))$ , or $y - 2 = 4(x + 1)\textsf{.}$

Practice playmedium

Solve $e^{-x}=6$ for the real value of $x$ .

Take $\ln$ of both sides: $-x=\ln 6$ . Since $-x=(-1)x$ , divide both sides by $-1$ to get $x=-\ln 6\textsf{.}$

Practice playeasy

The first five terms of an arithmetic sequence are $12, 18, 24, 30, 36$ . What is the $11$ th term?

The common difference is $d = 6$ . With $a_1 = 12$ , the $11$ th term is $a_{11} = 12 + 10(6) = 72$ .

Practice playmedium

Given $f(x)=x^{3}-5$ , which of the following is $f^{-1}(x)$ ?

Set $y=x^{3}-5$ . Swap: $x=y^{3}-5$ . Add $5$ : $x+5=y^{3}$ . Take the cube root: $y=\sqrt[3]{x+5}$ . So $f^{-1}(x)=\sqrt[3]{x+5}\textsf{.}$

DC CAPE Algebra II Building Functions. Practice it free.

Building Functions skills

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

Topics mapped to this domain

Exponential functions in context (SAT)

Exponential and log formulas

Linear functions from tables (ACT/SAT)

Linear rule from a function table (ACT)

Slope-point line equations (ACT/SAT/PSAT 8/9/10)

Solving exponential equations with logarithms (ACT)

Arithmetic sequence nth term

Finding inverse functions (ACT)

Function table composition (ACT)

Function transformation descriptions

Function transformations

Geometric sequence equations

8 free questions · 0/0 correct

Turn building functions into game time.

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