Question

Determine the domain and range of each function. Write in interval notation. f(x)=x^2-5

Answer 1

Well, the domain (the x value you plug into the function, for x) can be any number. It can be any positive or negative real number. Since there are no restrictions.
Domain (-∞,∞)

For the RANGE:
You can see that if x = 0 then you can get a range of -5 (this the y-intercept)
You won't get a smaller range than `-5` , see why ?
RANGE [-5,∞)

Answer 2

Does this make sense ?

Answer 3

yes. thank you. so for f(x)=-\[\sqrt{x-3}\]
domain: [-3,\[\infty\])
range: (-\[\infty\]]

Answer 4

sorry still new to this whole setup for the equation typing

Answer 5

You can type an infinity symbol, do you want to know how ?

Answer 6

I am on the keyboard and anywhere.....

1) Click and hold ALT

2) click the number code ` 2 3 6 `
(using the numbers that are on
the right of the keyboard, not the
ones below F1, F2, F3, etc., )

3) release the ALT (it should show ∞ )

Answer 7

∞ got it. thanks

Answer 8

Okay, but for \(\normalsize\color{blue}{ f(x)=-\sqrt{x-3}}\) The domain would be \(\normalsize\color{blue}{ [3,∞)}\) because if it is less than 3 you get an imaginary number.

The range will be \(\normalsize\color{blue}{ [0,∞)}\) because the smallest value you can get for `f(x)` is a 0 (at x=3) .