Patchwork PatFunction Machines · functions, their graphs, and sequences

A coat of patched pieces and a V-shaped collar: absolute value, piecewise and square root functions.

Absolute Value, Piecewise and Square Root Functions

Absolute value, piecewise and square root functions. In MathBound, the free Algebra I adventure game, Patchwork Pat asks these problems, and the only way past is to solve them.

Part of Linear Functions: chapter 5 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

Absolute Value Functions. Give the vertex of y = |x - h| + k.
Piecewise Functions. Evaluate or solve a two-piece function, or write |x - h| + k as two pieces.
Square Root Functions. Give the domain or range of y = sqrt(x - h) + k.
Inverse of a Linear Function. Find or use the inverse of f(x) = ax + b or of a relation, or say what an inverse value means.

Worked examples

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

Example 1 · Absolute Value Functions

What

is

the

minimum

value

of

y = ∣ x - 7 ∣ - 2 ?

$2$
$- 2$
$7$
$- 7$

Show the worked steps

$An$ $absolute$ $value$ $is$ $never$ $negative,$ $so$ $∣ x - 7 ∣$ $is$ $smallest,$ $0,$ $at$ $x = 7 .$
$Then$ $y = - 2,$ $the$ $minimum.$

Answer: $- 2$

Example 2 · Piecewise Functions

f (x) = {x + 3, 2 x - 6, x < 2 x \geq 2

Find

f (0) + f (4) .

$1$
$- 4$
$10$
$5$

Show the worked steps

$0 < 2,$ $so$ $f (0) = 3; 4 \geq 2,$ $so$ $f (4) = 2 .$
$f (0) + f (4) = 3 + 2 = 5 .$

Answer: $5$

Example 3 · Square Root Functions

What

is

the

domain

of

y = x + 3 ?

$x \leq - 3$
$x \geq 3$
$x > - 3$
$x \geq - 3$

Show the worked steps

$The$ $expression$ $under$ $the$ $root$ $cannot$ $be$ $negative:$ $x + 3 \geq 0.$
$So$ $x \geq - 3 .$

Answer: $x \geq - 3$

Where it is in your textbook

Textbook	Lessons
Standard course	5.7, 11.4, 11.5, 11.6
Big Ideas Math Algebra 1	3.7, 4.7, 10.1, 10.4
Big Ideas Math Algebra 1 (2022)	3.8, 4.7, 10.1, 10.4
Carnegie Learning Algebra I	M2 4.1, M2 4.3, M2 4.4, M2 4.5, M5 3.3
CPM Core Connections Algebra	1.2.2, 1.2.5, 11.1.2
CPS Skyline Algebra	8.1-8.2, 8.3-8.4, 8.5-8.6, 8.7
enVision Algebra 1	5-1, 5-2, 5-4, 10-1, 10-4, 10-5, 10-7
enVision Algebra 1 (2024)	5-1, 5-2, 5-4, 10-1, 10-4, 10-5, 10-7
Eureka Math Algebra I (EngageNY)	3.15-3.16, 3.17-3.20, 3.21-3.24, 4.18, 4.22
Glencoe Algebra 1	4-7, 9-7, 10-1
HMH Into Algebra 1	5.4, 8.1, 8.2
Illustrative Mathematics Algebra 1	4.10-4.11, 4.12, 4.13-4.14, 4.15-4.17
Illustrative Mathematics Algebra 1 (v.360)	5.10-5.11, 5.12, 5.13-5.14, 5.15-5.17
Math Nation Algebra 1 (Florida B.E.S.T.)	10.1, 10.2, 13.7
Pearson Algebra 1 Common Core	5-8, 10-5
Reveal Algebra 1	4-6, 4-7, 5-6
SpringBoard Algebra 1	10, 14

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