How do you graph y=5+3x−6 using asymptotes, intercepts, end behavior?

1 Answer
Rohan N.
Mar 31, 2018

Vertical asymptote is 6
End behaviour (horizontal asymptote) is 5
Y intercept is −72
X intercept is 275

Explanation:

We know that the normal rational function looks like 1x

What we have to know about this form is that it has a horizontal asymptote (as x approaches ±∞) at 0 and that the vertical asymptote (when the denominator equals 0) is at 0 as well.

Next we have to know what the translation form looks like

1x−C+D

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

0=5+3x−6

−5=3x−6

−5(x−6)=3

−5x+30=3

x=−27−5

So you have the co-ordiantes (275,0)

To find the y intercept set x to 0

y=5+30−6

y=5+1−2

y=72

So we get the co-ordiantes (0,72)

So sketch all of that to get
graph{5+3/(x-6) [-13.54, 26.46, -5.04, 14.96]}

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