i'm asked to find the domain of these problems
(0,2) (3,5)
y=5-x
y= square root x+4
I know with fun. the domain is all IR, but is there a way to solve the problems?
the domain is the set of all inputs for which a function is defined. when written as ordered pairs, the domain is the set of the first elements in the ordered pair.
For $\displaystyle \{ (0,2), (3,5) \}$ the domain is $\displaystyle \{ 0,3 \}$
since those are the first elements of the ordered pairs
$\displaystyle y = 5 - x$
we can input anything for x here. this is a polynomial, and so, the domain is given by: $\displaystyle \mbox{dom}f = \mbox{dom}y = \{ x | x \in \mathbb{R} \} = (-\infty, \infty)$
For $\displaystyle \sqrt{x + 4}$ we have a restriction. we can only input the x-values that ensure that what is being square rooted is non-negative. thus we require $\displaystyle x + 4 \ge 0$
so what is the domain of the function here?