Anatomy of a Rational Function

Drag to graph Analyze . Drag the labels to their correct features.

Intervals of Decrease

Adjust sliders Find the interval where is strictly decreasing.

{{ (i-7)/2 }}
Selected Interval:

Asymptotic Growth Rates

Slide & Tap Compare growth as . Slide x to 12, then tap to rank from fastest (1st) to slowest (3rd).

x = {{ s3_x }}
{{ fn.rank ? fn.rank : '?' }}
{{ formatNumber(fn.val) }}

Function Builder

Tap to build Construct f(x) with a Vertical Asymptote at and Horizontal Asymptote at .

f(x) =
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Masterful Analysis!

You've successfully dissected rational functions, identified intervals, compared growth rates, and built functions from scratch.