Number MillFunction Machines · functions, their graphs, and sequences

Grinds an input into its output: function notation, and one relationship as a rule, a table, a graph and a story.

Function Notation

Function notation, and one relationship as a rule, a table, a graph and a story. In MathBound, the free Algebra I adventure game, Number Mill asks these problems, and the only way past is to solve them.

Part of Functions: chapter 4 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Evaluate a Function. Evaluate a linear function at an integer, or read and write f(a) = b in a story.
Linear or Nonlinear. Pick the equation or the situation that is, or is not, a linear function.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Evaluate a Function

W (d)

is

the

water,

in

liters,

left

in

a

leaking

tank

d

days

after

the

leak

began.

Which

statement

in

function

notation

says

this?

After

2

days,

89

liters

of

water

are

left

in

the

tank.

$W (0) = 89$
$W (2) = 89$
$W (d) = 89$
$W (89) = 2$

Show the worked steps

$The$ $input$ $inside$ $the$ $brackets$ $is$ $the$ $value$ $of$ $d : 2 .$ $The$ $output,$ $after$ $the$ $equals$ $sign,$ $is$ $89.$
$So$ $W (2) = 89 .$

Answer: $W (2) = 89$

Example 2 · Linear or Nonlinear

Is

y = x^{2} - 7

a

linear

function?

$No:$ $x$ $is$ $in$ $a$ $denominator$
$No:$ $x$ $is$ $squared$
$No:$ $x$ $is$ $an$ $exponent$
$Yes:$ $it$ $can$ $be$ $written$ $as$ $y = m x + b$

Show the worked steps

$A$ $linear$ $function$ $can$ $be$ $written$ $as$ $y = m x + b,$ $with$ $x$ $to$ $the$ $first$ $power$ $only.$
$y = x^{2} - 7$ $cannot:$ $No:$ $x$ $is$ $squared .$

Answer: $No:$ $x$ $is$ $squared$

Example 3 · Evaluate a Function

W (d)

is

the

water,

in

liters,

left

in

a

leaking

tank

d

days

after

the

leak

began.

What

does

W (5) = 30

mean?

$The$ $tank$ $loses$ $30$ $liters$ $during$ $day$ $5.$
$The$ $tank$ $loses$ $30$ $liters$ $each$ $day.$
$After$ $5$ $days,$ $30$ $liters$ $of$ $water$ $are$ $left$ $in$ $the$ $tank.$
$After$ $30$ $days,$ $5$ $liters$ $of$ $water$ $are$ $left$ $in$ $the$ $tank.$

Show the worked steps

$In$ $W (5) = 30,$ $the$ $input$ $d$ $is$ $5$ $and$ $the$ $output$ $is$ $30.$
$So:$ $After$ $5$ $days,$ $30$ $liters$ $of$ $water$ $are$ $left$ $in$ $the$ $tank.$

Answer: $After$ $5$ $days,$ $30$ $liters$ $of$ $water$ $are$ $left$ $in$ $the$ $tank.$

Where it is in your textbook

Textbook	Lessons
Standard course	4.3, 4.4, 11.6
Big Ideas Math Algebra 1	3.2, 3.3, 10.4
Big Ideas Math Algebra 1 (2022)	3.3, 3.4, 10.4
Carnegie Learning Algebra I	M1 1.2, M1 1.3
CPM Core Connections Algebra	1.1.2, 1.1.3, 1.2.3, 1.2.4, 2.1.1, 2.2.3, 5.1.1, 8.2.1, 11.1.2, 11.3.2
CPS Skyline Algebra	2.1-2.2, 2.3, 3.4, 3.5, 6.1-6.2, 8.7
enVision Algebra 1	3-2, 6-2, 10-7
enVision Algebra 1 (2024)	3-2, 6-3, 10-7
Eureka Math Algebra I (EngageNY)	3.9-3.10
Glencoe Algebra 1	1-7, 3-1, 4-7
HMH Into Algebra 1	4.1, 4.2, 13.2, 20.2
Holt McDougal Larson Algebra 1	1.7, 1.8, 3.2, 3.7
Illustrative Mathematics Algebra 1	4.1-4.3, 4.4-4.5, 4.15-4.17, 4.18, 5.1-5.2, 5.19-5.20, 6.3-6.4, 6.5-6.7
Illustrative Mathematics Algebra 1 (v.360)	5.1-5.3, 5.4-5.5, 5.15-5.17, 5.18, 6.1-6.2, 6.19-6.20, 7.3-7.4, 7.5-7.7
Math Nation Algebra 1 (Florida B.E.S.T.)	1.2, 1.3, 4.6, 4.7
MVP Mathematics I (Integrated Math 1)	2.1, 3.4, 3.5
Open Up NC Math 1 (MVP)	2.1, 3.4, 3.5, 6.3
Pearson Algebra 1 Common Core	4-3, 4-4, 4-5, 4-6, 7-6
Reveal Algebra 1	3-2, 3-3, 5-6, 9-1
SpringBoard Algebra 1	5, 9

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