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

Mar 31, 2017

Domain: $\left(- \infty , \infty\right)$
Range: $\left[- 2 , \infty\right)$

#### Explanation:

$f \left(x\right) = {x}^{4} + {x}^{2} - 2$

The domain of polynomial equations is $x \in \left(- \infty , \infty\right)$

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 $\infty$.

$f ' \left(x\right) = 4 {x}^{3} + 2 x$

$f ' \left(x\right) = 2 \left(x\right) \left({x}^{2} + 1\right)$

$0 = f ' \left(x\right)$

$0 = 2 \left(x\right) \left({x}^{2} + 1\right)$

$x = 0$

$f \left(0\right) = - 2$

Range:$\left[- 2 , \infty\right]$