Find the zeros, vertical asymptote, horizontal asymptote, slant asymptote, and graphing points. (x + 4)/(x^2 + x - 6)

Question

Find the zeros, vertical asymptote, horizontal asymptote, slant asymptote, and graphing points.


`(x + 4)/(x^2 + x - 6)`

Answer 1

first, simplify fraction
(x+4)/((x-2)(x+3))
good
set numerator to zero
x+4=0
x=-4

VA
set denom to zero
(x-2)(x+3)=0
VA's at x=-3 and x=2

HA
for p(x)/q(x)
degreee of p(x)<q(x)
HA=0
no slant asymtote
does it cross HA?
0=(x+4)/(x^2+x-6)
0=x+4
-4=x
it crosses at (-4,0)

to graph
plot point (-4,0)
draw assymtotes
y=0
x=2
x=-3

go from top left to middle botttom to top right
reverse 'L' on top left going through (-4,0)
upside down 'U' at middle
'L' at right top