How do you find the domain and range of $y = - \frac{3}{4 x + 4}$ $y=-3/(4x+4)$ ?

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Answer 1 · 2017-06-08T02:07:13

Domain: $(- \infty, - 1) \cup (- 1, + \infty)$ $(-oo,-1)uu(-1,+oo)$
Range: $(- \infty, + \infty)$ $(-oo,+oo)$

$y = - \frac{3}{4 x + 4}$ $y = -3/(4x+4)$

$y$ $y$ is defined for all real x except where $4 x + 4 = 0$ $4x+4 =0$
i.e where $x = - 1$ $x=-1$

$:. y$ is defined $forall x in RR: x!= -1$

Hence the domain of $y$ is $(-oo,-1)uu(-1,+oo)$

$Lim_"x->-1 (-)" y = +oo$

and

$Lim_"x->-1 (+)" y = -oo$

Hence the range of $y$ is $(-oo,+oo)$

This can be seen by the graph of $y$ below.
graph{-3/(4x+4) [-10, 10, -5, 5]}

How do you find the domain and range of y=-3/(4x+4) y=−34x+4y=-3/(4x+4) ?