How do you graph $f(x)=3/x+1$ using holes, vertical and horizontal asymptotes, x and y intercepts?

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Answer 1 · 2017-12-05T19:06:31

See below.

y axis intercepts occur when $x=0$ . $x=0$ is undefined for this function, so no y intercept.

x axis intercepts occur when $y=0$ :

$3/x+1=0=>x=-3$

Coordinate: $( -3 , 0 )$

as $x->oo$ , $color(white)(888)3/x+1->1$

as $x->-oo$ , $color(white)(888)3/x+1->1$

The line $y=1$ is a horizontal asymptote.

as $x->0^+$ , $color(white)(888)3/x+1->oo$

as $x->0^-$ , $color(white)(888)3/x+1->-oo$

The line $x=0$ is a vertical asymptote.

Graph:

enter image source here

How do you graph f(x)=3/x+1f(x)=3/x+1 using holes, vertical and horizontal asymptotes, x and y intercepts?