Marbleslides Rationals !!exclusive!! -

Here lies the first twist. Unlike a line or a parabola, a rational function is not a single, continuous stroke. It is a creature of two halves. It has a gap—a great, invisible wall through which no marble can pass. This is the vertical asymptote.

$$y = \fracax - h + k$$

In a traditional textbook, students learn to graph $y = 1/x$ or its transformations by creating a table of values. They plot points, connect the dots, and usually make a critical error: they draw a straight line right through the y-axis, turning two separate curves into a single, confused squiggle. marbleslides rationals

This introduces the concept of .

Students must learn to restrict their equation to a specific range of $x$-values. For example: $$y = \frac1x - 3 + 2 x < 3$$ Here lies the first twist

Anyone can start sliding the graph, but the later "Challenge" screens require deep algebraic knowledge. It has a gap—a great, invisible wall through