How do you graph y=(8-5x)/(x-5) using asymptotes, intercepts, end behavior?
1 Answer
see explanation.
Explanation:
color(blue)"Asymptotes" 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-5=0rArrx=5" is the asymptote" Horizontal asymptotes occur as
lim_(xto+-oo),ytoc" ( a constant)" divide terms on numerator/denominator by x
y=(8/x-(5x)/x)/(x/x-5/x)=(8/x-5)/(1-5/x) as
xto+-oo,yto(0-5)/(1-0)
rArry=-5" is the asymptote" Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (both of degree 1 ) Hence there are no oblique asymptotes.
color(blue)"Intercepts"
x=0toy=8/(-5)rArr(0,-8/5)
y=0rArr8-5x=0rArrx=8/5rArr(8/5,0)
graph{(8-5x)/(x-5) [-20, 20, -10, 10]}
