Find the range without graphing?

Question

how can you find the range of 12/(x+7) without graphing

Answer 1

okay u should specify the domain of x,assuming x is real positive.

first keep x=0 u get 1.7

then put x= infinity u get zero

so the range is 0 to 1.7

Answer 2

y = 12 / (x + 7) is valid for all x except x = - 7, which makes the denominator zero.

As x -> infty, y -> 0.

As x -> - infty, y -> 0.

As x approaches - 7 from above, y -> infty.

As x approaches - 7 from below, y -> - infty.

The range is (- infty, - 7) U (- 7, infty).