Near-Miss MothFractioneers · rational expressions and functions

Flies ever closer to the lamp and never touches it: graphs of rational functions.

Rational Functions

Graphs of rational functions. In MathBound, the free Algebra I adventure game, Near-Miss Moth asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

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

What you will practice

Graphs of Rational Functions. Give the excluded value or vertical asymptote of y = a/(x - h), or use inverse variation.

Worked examples

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

Example 1 · Graphs of Rational Functions

What

is

the

vertical

asymptote

of

the

graph

of

y = \frac{3}{x - 4} ?

$x = 4$
$x = - 4$
$x = 3$
$y = 4$

Show the worked steps

$The$ $graph$ $has$ $a$ $vertical$ $asymptote$ $where$ $the$ $denominator$ $is$ $0.$
$x - 4 = 0$ $at$ $x = 4 :$ $the$ $asymptote$ $is$ $x = 4 .$

Answer: $x = 4$

Example 2 · Graphs of Rational Functions

What

value

of

x

is

excluded

from

the

domain

of

y = \frac{1}{x - 4} + 4 ?

$x = 4$
$x = - 4$
$x = 0$
$x = 1$

Show the worked steps

$The$ $denominator$ $x - 4$ $cannot$ $be$ $0.$
$x - 4 = 0$ $when$ $x = 4,$ $so$ $x = 4$ $is$ $excluded.$

Answer: $x = 4$

Example 3 · Graphs of Rational Functions

What

are

the

asymptotes

of

the

graph

of

y = \frac{- 3}{x + 4} - 6 ?

$x = - 6$ $and$ $y = - 4$
$x = - 4$ $and$ $y = - 6$
$x = - 4$ $and$ $y = 6$
$x = 4$ $and$ $y = - 6$

Show the worked steps

$Vertical:$ $the$ $denominator$ $is$ $0$ $at$ $x = - 4 .$
$Horizontal:$ $the$ $fraction$ $shrinks$ $toward$ $0,$ $leaving$ $y = - 6 .$

Answer: $x = - 4$ $and$ $y = - 6$

Where it is in your textbook

Textbook	Lessons
Glencoe Algebra 1	11-1, 11-2
Pearson Algebra 1 Common Core	11-7

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