Question

What is the domain and range of `y=x^4+x^2-2`?

Answer 1

Domain: `(-oo,oo)`
Range: `[-2,oo)`

Explanation:

`f(x)=x^4+x^2-2`

The domain of polynomial equations is `x in (-oo,oo)`

Since this is equation has an even highest degree of 4, the lower bound of the range can be found by determining the absolute minimum of the graph. The upper bound is `oo`.

`f'(x)=4x^3+2x`

`f'(x)=2(x)(x^2+1)`

`0=f'(x)`

`0=2(x)(x^2+1)`

`x=0`

`f(0)=-2`

Range:`[-2,oo]`