What is the domain and range of $y = \frac{3}{x}$ $y = 3/x$ ?

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Answer 1 · 2017-07-12T13:49:02

See below.

Domain: you shall not divide by zero: $RR - {0}$

Image: by the hyperbola graph, $RR - {0}$

Answer 2 · 2017-07-12T14:12:16

Domain: $(-oo, 0)uu(0, +oo)$
Range: $(-oo, +oo)$

$y = 3/x$

$y$ is defined $forall x in RR: x!=0$

Hence the domain of $y$ is $(-oo, 0)uu(0, +oo)$

Now consider:

$lim_"x->0-"y =-oo$

and

$lim_"x->0+"y =+oo$

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

This can be seen from the graph of $y$ below.

graph{3/x [-10, 10, -5, 5]}

What is the domain and range of y = 3/xy=3xy = 3/x?