End Behavior, and the Line a Graph Settles Onto

You'll learnto compare the degrees before choosing a rule, to read a horizontal asymptote as a claim about the far ends rather than a fence, and to compute both ends whenever an even root is in play.

A horizontal asymptote is a claim about the two far ends of a graph. The window here never moves; instead two dots travel outward and the gap between the curve and the level is what shrinks. Which degree wins decides the level, a curve may cross it, and the two ends need not agree. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · THREE CASES · TWO ENDS · A LINE THAT MAY BE CROSSED · v2

the target is at the ends of the axis, so compare the degrees, then check both ends

Before you start

What you're looking at

One graph in a window that never moves. Two dots leave the middle and travel outward, amber to the left and violet to the right, each dragging a short dashed gap to a level line.

The question

Where are the outputs heading as the inputs run away in each direction?

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