How do you graph $f( x ) = \frac { x + 3} { x ^ { 2} - 2x - 63}$ ?

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Answer 1 · 2018-01-23T23:29:17

asymptotes: $x = -7, x = 9$
$x-$ intercept: $(3,0)$
$y-$ intercept: $(0, - 1/21)$

firstly, factorise $x^2-2x-63$ :

$7+( -9) = -2$

$7 *( -9) = -63$

$x^2-2x-63 = (x+7)(x-9)$

$(x+3)/(x^2-2x-63) = (x-3)/((x+7)(x-9))$

in this form, it is easier to find any asymptotes that there may be.

noting that $n/0=$ undefined:

$(x-3)/(x+7)$ is undefined
when $x=-7, x+7 = 0$
this means that the graph cannot go through the line $x=-7$ .

$(x-3)/(x-9)$ is undefined
when $x=9, x-9 = 0$
this means that the graph cannot go through the line $x= 9$ .

to plot the $x-$ intercept:

use $0/n = 0$

the numerator in the function is $x-3$ .

$y = 0$ when $x-3=0$ , so $y=0$ when $x=3$ .

this means that the coordinates of the $x-$ intercept are $(3,0)$ .

to plot the $y-$ intercept:

set $x$ to $0$ .

$(x-3)/((x+7)(x-9)) = (-3)/(7*-9) = -(3)/(63) = -1/21$

when $x = 0$ , $y = - 1/21$

this means that the coordinates of the $y-$ intercept are $(0, - 1/21)$

graph{(x-3)/((x+7)(x-9)) [-10, 10, -5, 5]}

How do you graph f( x ) = \frac { x + 3} { x ^ { 2} - 2x - 63}f( x ) = \frac { x + 3} { x ^ { 2} - 2x - 63}?