How do you graph $f (x) = - \frac{2}{x}$ $f(x)=-2/x$ using holes, vertical and horizontal asymptotes, x and y intercepts?

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Answer 1 · 2017-09-30T09:28:36

See below.

$y = - \frac{2}{x}$ $y = -2/x$

$y$ $y$ axis intercepts occur where $x = 0$ $x=0$

$y = - \frac{2}{0}$ $y= -2/(0)$ Undefined (Division by zero):

$x$ $x$ axis intercepts occur where $y = 0$ $y=0$ :

$0 = - \frac{2}{x}$ $0=-2/x$

Solving for $x$ $x$

$0 x = - 2 \Rightarrow 0 \neq - 2$ $0x = -2=> 0!= -2$

No intercepts of $x$ $x$ axis:

As $x \to \infty$ $x-> oo$

$- \frac{2}{x} \to 0$ $-2/x-> 0$

As $x \to - \infty$ $x->-oo$

$- \frac{2}{x} \to 0$ $-2/x-> 0$

$x$ $x$ axis is a horizontal asymptote.

Left hand limit:

$lim_(x->0^-)-2/x->oo$

Right hand limit:

$lim_(x->0^+)-2/x->-oo$

$y$ axis is a vertical asymptote.

Graph of $y=-2/x$

graph{y=-2/x [-10, 10, -10, 10]}

How do you graph f(x)=-2/xf(x)=−2xf(x)=-2/x using holes, vertical and horizontal asymptotes, x and y intercepts?