Family-Tree FernFunction Machines · functions, their graphs, and sequences

Keeps a locket of family portraits: parent functions.

Function Families

Parent functions. In MathBound, the free Algebra I adventure game, Family-Tree Fern asks these problems, and the only way past is to solve them.

Part of Radicals and More Functions: chapter 11 of the standard course.

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

What you will practice

Parent Functions. Name the parent function (linear, quadratic, absolute value, square root, cube root, cubic, exponential) of an equation, graph or table.
End Behavior and Symmetry. Describe the end behavior of a linear, quadratic, cubic or exponential function.

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

Which

parent

function,

shifted

up

or

down,

gives

this

table?

x y 00112337415

Show the worked steps

$Subtract$ $- 1$ $from$ $each$ $output$ $(if$ $it$ $was$ $shifted)$ $and$ $compare$ $with$ $the$ $parents.$
$The$ $outputs$ $1, 2, 4, 8, 16$ $come$ $from$ $the$ $exponential$ $parent.$

Answer: $exponential$

f (x) = 2^{x} . As

x \to \infty,

what

happens

to

f (x)?

Show the worked steps

Answer: $f (x) \to \infty$

Its

graph

starts

at

an

endpoint

and

rises

more

and

more

slowly;

its

domain

is

x \geq 0 .

Which

parent

function

is

it?

Show the worked steps

Answer: $square$ $root$

Textbook	Lessons
Standard course	11.4
Big Ideas Math Algebra 1	8.4, 10.2
Big Ideas Math Algebra 1 (2022)	8.4, 10.2
Carnegie Learning Algebra I	M1 1.4
CPM Core Connections Algebra	1.2.2, 11.1.1
CPS Skyline Algebra	8.7
enVision Algebra 1	10-2, 10-3
enVision Algebra 1 (2024)	10-2, 10-3
Eureka Math Algebra I (EngageNY)	4.18, 4.22, 5.1
HMH Into Algebra 1	20.4
Math Nation Algebra 1 (Florida B.E.S.T.)	1.1, 8.1, 11.2, 13.3, 13.4, 13.H1
MVP Mathematics I (Integrated Math 1)	3.3, 3.6
Open Up NC Math 1 (MVP)	3.3