How do you graph y=(7x)/(-x-15) using asymptotes, intercepts, end behavior?
1 Answer
Dec 12, 2016
see explanation.
Explanation:
The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.
solve :
-x-15=0rArrx=-15" is the asymptote" Horizontal asymptotes occur as
lim_(xto+-oo),ytoc" (a constant)" divide terms on numerator/denominator by x
y=((7x)/x)/(-x/x-15/x)=7/(-1-15/x) as
xto+-oo,yto7/(-1-0)
rArry=-7" is the asymptote" Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here ( both degree 1) Hence there are no oblique asymptotes.
color(blue)"Intercepts"
x=0toy=0/(-15)=0rArr(0,0)
y=0to7x=0rArr(0,0)
graph{(7x)/(-x-15) [-40, 40, -20, 20]}
