Question

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` ?

Answer 1

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`