How do you graph #y=(7x)/(-x-15)# using asymptotes, intercepts, end behavior?

1 Answer
Dec 12, 2016

Answer:

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]}