Mash-Up MarloFunction Machines · functions, their graphs, and sequences

Cranks two hoppers into one grinder: operations with functions.

Operations with Functions

Operations with functions. In MathBound, the free Algebra I adventure game, Mash-Up Marlo asks these problems, and the only way past is to solve them.

Part of Radicals and More Functions: chapter 11 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

Function Operations. Find (f + g)(x) or (f - g)(x) for linear and quadratic functions.

Worked examples

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

Example 1 · Function Operations

f (x) = - 4 x - 7

and

g (x) = - 6 x + 3 .

Ana

wrote

(f - g) (x) = 2 x - 4 .

What

should

it

be?

$- 2 x + 10$
$2 x - 10$
$2 x - 4$
$- 10 x - 4$

Show the worked steps

$Ana$ $subtracted$ $only$ $the$ $x$ $term$ $of$ $g;$ $the$ $constant$ $3$ $must$ $change$ $sign$ $too.$
$(f - g) (x) = 2 x - 10 .$

Answer: $2 x - 10$

Example 2 · Function Operations

f (x) = - 6 x - 3

and

g (x) = x + 9 .

Find

(g - f) (x) .

$- 7 x - 12$
$- 5 x + 6$
$7 x + 12$
$7 x + 6$

Show the worked steps

$(g - f) (x)$ $is$ $g (x) - f (x),$ $in$ $that$ $order:$ $(x + 9) - (- 6 x - 3) .$
$Combine$ $like$ $terms:$ $7 x + 12 .$

Answer: $7 x + 12$

Example 3 · Function Operations

f (x) = 2 x

and

g (x) = - 5 x - 4 .

Find

(f \cdot g) (x) .

$- 10 x^{2} - 4$
$- 3 x - 4$
$- 10 x - 8$
$- 10 x^{2} - 8 x$

Show the worked steps

$Distribute$ $2 x$ $over$ $- 5 x - 4 .$
$(f \cdot g) (x) = - 10 x^{2} - 8 x .$

Answer: $- 10 x^{2} - 8 x$

Where it is in your textbook

Textbook	Lessons
Standard course	11.6
CPS Skyline Algebra	3.5
enVision Algebra 1	10-6
enVision Algebra 1 (2024)	10-6
HMH Into Algebra 1	20.2
Math Nation Algebra 1 (Florida B.E.S.T.)	13.H2
MVP Mathematics I (Integrated Math 1)	3.4, 3.5
Open Up NC Math 1 (MVP)	3.4, 3.5, 7.2
Reveal Algebra 1	11-9

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