Question

How do you find the domain and range of $y={{x}^{2}}$?

Answer 1

For solving these types of questions, to get the domain of the function we need to simply look for the values of $x$ which will satisfy the equation and the range of the equations is simply the values of $y$.

Complete Step by Step Solution:
As we know, for the domain the range of values that can be substituted for $x$ in a function
In this case, $x$ needs to have an existing square to be part of the domain of the function $y={{x}^{2}}$.
As any number can be squared, including positive and negative numbers and π.

This means that the domain goes from $-\infty$ to $\infty$, which can be written as $\left( -\infty ,\infty \right)$.

The range of values that $y$ can be a function, in this case, $y$ can be any positive number, including $0$.
It will always be positive since the squares of negative numbers are also positive.

Which means that the range goes from $0$ to $\infty$, which can be written as $\left( 0,\infty \right)$.

Note:
Domain: The range of values that can be substituted for $x$ in a function.
Range: Range of values that $y$ can be in a function.