What is the end behavior of f(x)=6x^3+1f(x)=6x3+1?

1 Answer
Psykolord1989 . · Jim G.
Sep 8, 2017

It tends towards -oo−∞ on the left, and oo∞ on the right. graph{6x^3+1 [-10, 10, -5, 5]}

Explanation:

This is simply an x^3x3 function that has experienced a veradical stretch by a factor of 6 (our x^3x3 coefficient), and a vertical shift of 1 unit upwards (from the +1). Neither of these alterations change the end behavior; if our 6 were instead -6, that would have an effect, but the coefficient is instead positive.

The elementary x^3x3 function tends towards oo∞ as x->oox→∞ (i.e., to the right), and towards -oo−∞ as x->-oox→−∞ (to the left). If you wish to test this, choose an arbitrarily large constant k>0k>0. k^3k3 will be positive, because k was positive, and there is no negative coefficient. On the other hand, (-k)^3(−k)3 will be negative, because a negative number cubed returns a negative.

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