# How do you find the domain and range of y=2x^2+1?

Apr 27, 2017

Domain: All real numbers
Range: $y > 1$

#### Explanation:

Normally, $x$ or $y$ will be limited if there are fractions or square roots.

$x$ is not limited to any numbers. That means the domain is all real numbers.

Solve for $y$ to figure out the range:

$y - 1 = 2 {x}^{2}$

$\frac{y - 1}{2} = {x}^{2}$

$\sqrt{\frac{y - 1}{2}} = x$

$y$ is in a square root this time and we need to figure out the limitations. A square root cannot have negative numbers. So:

$\frac{y - 1}{2} > 0$

Solve for $y$:

$y - 1 > 0$

$y > 1$