Question

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

Answer 1

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]}