Find a polynomial function if Y-intercept is (0,1) .If there are no X-intercepts . Degree is 4 and End behaviour is xrarr-oo,f(x)rarr oo and xrarr oo,f(x)rarr oo ?

1 Answer
Dec 3, 2017

There are infinitely many such functions.

Explanation:

One is x^4 + 1

Another is 1/2(x-1)^2(x+1)^2+1/2

And 1/8(x+1)^2(x-2)^2+1/2

And two more for good measure

1/162(x-3)^4+1/2

1/240(4+4)(x+1)(x-3)(x-5)+3/4