Homework Help

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

user profile pic

sarcasticbrun... | Student | Honors

Posted April 19, 2012 at 9:30 PM via web

dislike 0 like

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

2 Answers | Add Yours

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted April 19, 2012 at 9:46 PM (Answer #1)

dislike 2 like

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.

Top Answer

user profile pic

rcmath | High School Teacher | (Level 1) Associate Educator

Posted April 19, 2012 at 11:18 PM (Answer #2)

dislike 1 like

An algebraic method to find the range.

`x^2>=0=>`

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

`y>=-5`

Hence the range is `[-5,oo)`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes