Same Function, Different Outfit

You'll learnto choose the form of an expression — factored, standard, or divided — that answers your question fastest.

Equivalent forms agree at every shared input and read nothing alike. Factored form hands you the zeros, standard form the ends, and divided form what a rational function imitates far out, which is where the asymptote rules actually come from.

8 STEPS · 6 QUICK CHECKS · FACTORED / STANDARD / DIVIDED · ASYMPTOTES · v2

divide when the ends matter, factor when the zeros do

Before you start

What you're looking at

One expression shown three ways at once, each with the question it answers written above it.

The question

Do you need the zeros, the ends, or what the function imitates far away?

Watch for

One full long division — labeled dividend, divisor, quotient, remainder — before it is used to explain an asymptote.

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