Growth RacerFunction Machines · functions, their graphs, and sequences

Races a steady car, a curving one and a rocket: linear, quadratic and exponential models.

Linear, Quadratic and Exponential Models

Linear, quadratic and exponential models. In MathBound, the free Algebra I adventure game, Growth Racer 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

Which Kind of Function?. Name a table as linear or exponential from its differences or ratios.
Differences and Ratios. Find the constant first difference of a linear table, or the growth and rule of a tile pattern.
Which Grows Fastest?. Pick the function that eventually exceeds the others.

Worked examples

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

Example 1 · Which Kind of Function?

Does

the

table

show

a

constant

difference,

a

constant

factor,

or

neither?

x y 0481242123643

$a$ $constant$ $difference$ $of$ $- 24$
$a$ $constant$ $factor$ $of$ $\frac{1}{2}$
$neither$
$a$ $constant$ $difference$ $of$ $24$

Show the worked steps

$The$ $differences$ $are$ $- 24, - 12, - 6, - 3,$ $and$ $the$ $ratios$ $are$ $\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2} .$
$The$ $ratios$ $stay$ $the$ $same :$ $a$ $constant$ $factor$ $of$ $\frac{1}{2} .$

Answer: $a$ $constant$ $factor$ $of$ $\frac{1}{2}$

Example 2 · Differences and Ratios

The

points

(0, - 8), (1, - 2), (2, 4), (3, 10), (4, 16)

lie

on

a

line.

By

how

much

does

y

change

each

time

x

goes

up

by

1 ?

$- 8$
$- 6$
$- 2$
$6$

Show the worked steps

$Subtract$ $each$ $y$ $from$ $the$ $next:$ $6, 6, 6, 6 .$
$The$ $constant$ $difference$ $is$ $6 .$

Answer: $6$

Example 3 · Which Grows Fastest?

Why

does

3^{x}

eventually

pass

60 x ?

$3^{x}$ $multiplies$ $by$ $3$ $each$ $step,$ $while$ $60 x$ $only$ $adds$ $60$
$They$ $grow$ $at$ $the$ $same$ $rate$ $after$ $x = 3$
$3^{x}$ $is$ $already$ $larger$ $at$ $x = 1$
$60 x$ $starts$ $larger,$ $so$ $it$ $stays$ $larger$

Show the worked steps

$60 x$ $goes$ $up$ $by$ $the$ $same$ $60$ $every$ $step.$
$3^{x}$ $is$ $multiplied$ $by$ $3$ $every$ $step,$ $so$ $its$ $steps$ $keep$ $getting$ $bigger$ $and$ $eventually$ $beat$ $any$ $fixed$ $amount.$

Answer: $3^{x}$ $multiplies$ $by$ $3$ $each$ $step,$ $while$ $60 x$ $only$ $adds$ $60$

Where it is in your textbook

Textbook	Lessons
Standard course	4.4, 9.7
Big Ideas Math Algebra 1	6.3, 8.6
Big Ideas Math Algebra 1 (2022)	6.3, 8.6
Carnegie Learning Algebra I	M1 1.3, M3 1.1, M3 2.4, M5 1.4, M5 3.3
CPM Core Connections Algebra	1.1.2, 2.1.1, 5.1.1, 5.3.1, 6.2.5, 7.1.6, 7.2.3, 11.3.5
CPS Skyline Algebra	1.7, 2.3, 2.8, 6.1-6.2, 6.3, 6.5, 6.6
enVision Algebra 1	6-2, 6-3, 8-5
enVision Algebra 1 (2024)	6-3, 6-4, 8-5
Eureka Math Algebra I (EngageNY)	1.1-1.3, 3.14, 3.21-3.24, 5.1, 5.2, 5.3, 5.6-5.7
Glencoe Algebra 1	3-5, 7-5, 9-6
HMH Into Algebra 1	13.2, 19.5, 20.1
Holt McDougal Larson Algebra 1	9.8, 9.9
Illustrative Mathematics Algebra 1	5.1-5.2, 5.19-5.20, 5.21, 6.1-6.2, 6.3-6.4
Illustrative Mathematics Algebra 1 (v.360)	6.1-6.2, 6.19-6.20, 6.21, 7.1-7.2, 7.3-7.4
Math Nation Algebra 1 (Florida B.E.S.T.)	9.3, 11.1, 11.5, 13.3, 13.10
MVP Mathematics I (Integrated Math 1)	1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.8
Open Up NC Math 1 (MVP)	1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.6, 6.1, 6.2, 6.3, 6.5, 6.6
Pearson Algebra 1 Common Core	4-3, 9-7
Reveal Algebra 1	11-8
SpringBoard Algebra 1	7, 22, 34

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