# How do you find the domain and range for y = x^2-5?

Jul 3, 2016

the domain is $\mathbb{R}$, the range is $\left[- 5 , + \infty\right)$

#### Explanation:

Since y is a polynomial, its domain is $\mathbb{R}$

Then you find x:

${x}^{2} = y + 5$

that has two solutions:

$x = \pm \sqrt{y + 5}$

that are verified only if $y + 5 \ge 0$

or $y \ge - 5$

Then the range of y is $\left[- 5 , + \infty\right)$

You also can see the domain and the range in the graphic:

graph{x^2-5 [-10, 10, -5, 5]}

the domain, on x-axis, is all along the line,
the range begin in the y-coordinate -5 and continues to $+ \infty$