Flip-and-Slide FloFunction Machines · functions, their graphs, and sequences

An acrobat who slides, flips and stretches: transformations of functions and of figures.

Transformations of Functions

Transformations of functions and of figures. In MathBound, the free Algebra I adventure game, Flip-and-Slide Flo asks these problems, and the only way past is to solve them.

Part of Linear Functions: chapter 5 of the standard course.

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

What you will practice

Describe a Transformation. Describe g(x) = f(x) + k as a vertical shift, including moves of the line and exponential parents.

Worked examples

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

Example 1 · Describe a Transformation

The

graph

of

g

is

the

graph

of

f

after

a

shift

up

2

units .

Which

equation

gives

g ?

$g (x) = f (x) + 2$
$g (x) = f (x - 2)$
$g (x) = f (x + 2)$
$g (x) = f (x) - 2$

Show the worked steps

$Adding$ $or$ $subtracting$ $outside$ $the$ $function$ $moves$ $every$ $output,$ $so$ $the$ $graph$ $moves$ $vertically.$
$So$ $g (x) = f (x) + 2 .$

Answer: $g (x) = f (x) + 2$

Example 2 · Describe a Transformation

Compared

with

f (x) = 4^{x},

how

is

the

graph

of

g (x) = 4^{x} - 3

moved,

and

where

is

its

horizontal

asymptote?

$a$ $shift$ $down$ $3$ $units,$ $with$ $asymptote$ $y = - 3$
$a$ $shift$ $down$ $3$ $units,$ $with$ $asymptote$ $y = 3$
$a$ $shift$ $down$ $3$ $units,$ $with$ $asymptote$ $y = 0$
$a$ $shift$ $up$ $3$ $units,$ $with$ $asymptote$ $y = 3$

Show the worked steps

$Adding$ $or$ $subtracting$ $outside$ $the$ $function$ $moves$ $every$ $output,$ $so$ $the$ $graph$ $moves$ $vertically.$
$Every$ $output$ $moves$ $down$ $3,$ $the$ $asymptote$ $too:$ $from$ $y = 0$ $to$ $y = - 3 .$
$So:$ $a$ $shift$ $down$ $3$ $units,$ $with$ $asymptote$ $y = - 3 .$

Answer: $a$ $shift$ $down$ $3$ $units,$ $with$ $asymptote$ $y = - 3$

Example 3 · Describe a Transformation

Compared

with

f (x) = 4^{x},

how

is

the

graph

of

g (x) = 4^{x - 5}

moved,

and

where

is

its

horizontal

asymptote?

$a$ $shift$ $right$ $5$ $units,$ $with$ $asymptote$ $y = 5$
$a$ $shift$ $right$ $5$ $units,$ $with$ $asymptote$ $y = - 5$
$a$ $shift$ $left$ $5$ $units,$ $with$ $asymptote$ $y = 0$
$a$ $shift$ $right$ $5$ $units,$ $with$ $asymptote$ $y = 0$

Show the worked steps

$A$ $change$ $inside$ $the$ $function$ $moves$ $the$ $graph$ $horizontally,$ $the$ $opposite$ $way$ $to$ $its$ $sign.$
$Moving$ $sideways$ $does$ $not$ $change$ $how$ $close$ $the$ $outputs$ $get$ $to$ $0,$ $so$ $the$ $asymptote$ $stays$ $y = 0.$
$So:$ $a$ $shift$ $right$ $5$ $units,$ $with$ $asymptote$ $y = 0 .$

Answer: $a$ $shift$ $right$ $5$ $units,$ $with$ $asymptote$ $y = 0$

Where it is in your textbook

Textbook	Lessons
Standard course	5.7, 11.4
Big Ideas Math Algebra 1	3.6, 3.7, 10.1, 10.2
Big Ideas Math Algebra 1 (2022)	3.7, 3.8, 10.1, 10.2
Carnegie Learning Algebra I	M2 1.3, M2 4.1, M3 1.3
CPM Core Connections Algebra	11.1.1
CPS Skyline Algebra	7.1-7.2, 8.3-8.4
enVision Algebra 1	3-3, 5-4, 6-5, 10-2, 10-4, 10-5
enVision Algebra 1 (2024)	3-3, 5-4, 6-6, 10-2, 10-4, 10-5
Eureka Math Algebra I (EngageNY)	3.17-3.20, 4.19-4.21
Glencoe Algebra 1	10-1
HMH Into Algebra 1	5.1, 5.2, 8.2, 12.1
Holt McDougal Larson Algebra 1	3.7
Illustrative Mathematics Algebra 1	4.13-4.14
Illustrative Mathematics Algebra 1 (v.360)	5.13-5.14
Math Nation Algebra 1 (Florida B.E.S.T.)	13.5, 13.6, 13.7, 13.H1
MVP Mathematics I (Integrated Math 1)	3.6
Pearson Algebra 1 Common Core	5-8, 10-5
Reveal Algebra 1	4-4, 4-7, 9-2
SpringBoard Algebra 1	8

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