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.

Representations of a Relationship

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 More topics: taught by some textbooks beyond the usual course.

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

What you will practice

The Representations Web. Given a linear rule, table or situation, pick the matching rule, table or situation.

Worked examples

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

Example 1 · The Representations Web

Which

story

matches

y = 4 x + 12,

where

y

is

a

plant’s

height

in

centimeters

after

x

weeks?

$A$ $plant$ $12$ $centimeters$ $tall$ $that$ $grows$ $4$ $centimeters$ $a$ $week$
$A$ $plant$ $4$ $centimeters$ $tall$ $that$ $grows$ $12$ $centimeters$ $a$ $week$
$A$ $plant$ $12$ $centimeters$ $tall$ $that$ $shrinks$ $4$ $centimeters$ $a$ $week$
$A$ $plant$ $that$ $starts$ $at$ $0$ $centimeters$ $and$ $grows$ $16$ $centimeters$ $a$ $week$

Show the worked steps

$The$ $constant$ $12$ $is$ $the$ $height$ $at$ $x = 0,$ $the$ $start.$
$The$ $coefficient$ $4$ $is$ $the$ $growth$ $for$ $each$ $week.$

Answer: $A$ $plant$ $12$ $centimeters$ $tall$ $that$ $grows$ $4$ $centimeters$ $a$ $week$

Example 2 · The Representations Web

A

candle

is

40

centimeters

tall

and

burns

down

9

centimeters

an

hour.

Which

rule

gives

its

height

y

after

x

hours?

$y = - 9 x - 40$
$y = - 9 x + 40$
$y = 9 x + 40$
$y = 40 x - 9$

Show the worked steps

$The$ $amount$ $at$ $the$ $start,$ $x = 0,$ $is$ $40 :$ $the$ $y -intercept.$
$It$ $goes$ $down$ $9$ $for$ $each$ $step:$ $the$ $slope$ $is$ $- 9 .$

Answer: $y = - 9 x + 40$

Example 3 · The Representations Web

Which

list

of

points

lies

on

the

graph

of

y = 4 (2)^{x} ?

$(0, 2), (1, 8), (2, 32), (3, 128)$
$(0, 4), (1, 8), (2, 16), (3, 32)$
$(0, 1), (1, 8), (2, 64), (3, 512)$
$(0, 4), (1, 6), (2, 8), (3, 10)$

Show the worked steps

$At$ $x = 0, y = 4 (2)^{0} = 4 .$
$Each$ $step$ $of$ $1$ $multiplies$ $y$ $by$ $2 : 4, 8, 16, 32 .$

Answer: $(0, 4), (1, 8), (2, 16), (3, 32)$

Where it is in your textbook

Textbook	Lessons
MVP Mathematics I (Integrated Math 1)	2.11
Open Up NC Math 1 (MVP)	2.9, 6.6

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