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

Jul 12, 2017

See below.

Explanation:

Domain: you shall not divide by zero: $\mathbb{R} - \left\{0\right\}$

Image: by the hyperbola graph, $\mathbb{R} - \left\{0\right\}$

Jul 12, 2017

Domain: $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$
Range: $\left(- \infty , + \infty\right)$

Explanation:

$y = \frac{3}{x}$

$y$ is defined $\forall x \in \mathbb{R} : x \ne 0$

Hence the domain of $y$ is $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

Now consider:

${\lim}_{\text{x->0-}} y = - \infty$

and

${\lim}_{\text{x->0+}} y = + \infty$

Hence the range of $y$ is $\left(- \infty , + \infty\right)$

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

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