How do you graph #y=5+3/(x-6)# using asymptotes, intercepts, end behavior?
1 Answer
Vertical asymptote is 6
End behaviour (horizontal asymptote) is 5
Y intercept is
X intercept is
Explanation:
We know that the normal rational function looks like
What we have to know about this form is that it has a horizontal asymptote (as x approaches
Next we have to know what the translation form looks like
C~Horizontal translation, the vertical asympote is moved over by C
D~Vertical translation, the horizontal asympote is moved over by D
So in this case the vertical asymptote is 6 and the horizontal is 5
To find the x intercept set y to 0
So you have the co-ordiantes
To find the y intercept set x to 0
So we get the co-ordiantes
So sketch all of that to get
graph{5+3/(x-6) [-13.54, 26.46, -5.04, 14.96]}