Question

How do you find the range of a function?

Answer 1

Hint: In this problem, we can see about finding the range of a function. We should know that, if we are given a function with its domain, we can find the range of the given function. The set of all possible values that a function can attain is called its range. We can now see with an example.

Complete step-by-step solution:
Here we can see how to find the range of a function.
We should know that if we are given a function with its domain, we can find the range of the given function.
We know that all the possible values that x can take for which the given function is defined is called the domain of the function, where we will obtain different values for the function from putting different values from the domain.
Thus, the set of all possible values that a function can attain is called its range.
We can now find the range of function \[y=-{{x}^{2}}+1\], whose domain is \[\left\{ -1,0,1 \right\}\].
We can now find the range, by substituting the domain value in x and get y, we get
\[\begin{align}
  & \Rightarrow y=-{{\left( -1 \right)}^{2}}+1=0 \\
 & \Rightarrow y=-\left( 0 \right)+1=1 \\
 & \Rightarrow y=-\left( 1 \right)+1=0 \\
\end{align}\]
Therefore, the range of the function \[y=-{{x}^{2}}+1\] is \[R=\left\{ 0,1 \right\}\].

Note: We should always remember that the range of the function is obtained by substituting the domain value in x place of the given equation and getting the value of y. We should know that all the possible values that x can take for which the given function is defined is called the domain of the function and the set of all possible values that a function can attain is called its range.