For the function f(x)=x^2-5 find the domain and range.

Expert Answers
hala718 eNotes educator| Certified Educator

f(x)= x^2 - 5

The domain are all x values that has images.

As you see, we do not have any restrictions on the values of x .

==> Therefore, the domain is all real numbers.

As for the range, we need to find the range of the images.

You can easily find the range form looking at the graph by tracking the y-axis and see where the values are.

By looking at the graph ( y-axis) , we notice that the values of y ranges from -5 to infinity.

there are no values of y that is less than -5.

Therefore, the range is `y gt= -5.`  Or, all real numbers greater than or equal -5.

rcmath eNotes educator| Certified Educator

An algebraic method to find the range.

`x^2>=0=>`

`x^2-5>=-5=>`

`y>=-5`

Hence the range is `[-5,oo)`