Question

The rational function has a y-intercept of 7. What is the equation of this function?

Answer 1

Okay so I'm in Algebra II and the book shows how to graph a rational function like this y=x^2+x-12/x^2-4, by finding the horizontal asymptote and the vertical asymptotes y=(x+4)(x-3)/(x+2)(x-2), then when the numerator equals 0, y=(0+4)(0-3)/(0+2)(0-2) = 3 so the y-intercept is (0,3), so my q is how do I use the graph to find the equation! Can someone please explain the steps the book doesn't show!!

Answer 2

I guess work backwards.
Your graph as a y intercept (0,7).
you have a horizontal asymptote y=5 and a vertical asymptote x=-2

Answer 3

Okay, I'm not sure where to go from here, I mean then i find x and y-intercepts, look for holes, but how would i put this in an equation??

Answer 4

@phi do u know anyone who could teach this to me!?

Answer 5

I remember that if you divide by 0 you get a vertical asymptote

so to get an asymptote at x=-2 you want x+2 in the bottom , because -2+2 = 0 and we will divide by 0... creating an asymptote at x=-2

Answer 6

Awesome now how to i get the numerator, same concept??
(x-5)/(x+2), that seems too simple..

Answer 7

I am trying to remember what causes a horizontal asymptote
I guess you don't remember ?

Answer 8

So it says to find the horizontal asymptote of the graph of the rational function, compare the degree of the numerator m to the degree of the denominator n

If m<n, the graph has a horizontal asymptote y=0 (the x-axis)v
If m>n, the graph has no horizontal symptom
If m=n the graph has horizontal asymptote y=a/b

although i don't see how it relates...

Answer 9

the degree is the highest power (or number of (ax+b) factors )

you have a horizontal asymptote (Agree ??)
so we use
If m=n the graph has horizontal asymptote y=a/b

Answer 10

m=n y=a/b just to add to the last one a is the coefficient of the term of greatest degree in the numerator and b is the coefficient of the term of the greatest degree in the denominator

Answer 11

we know we have

(x+2)
in the bottom
the "b" they are talking about is the number in front of the x i.e. b=1

up top we want (a x + c )
then we will get a horizontal asymptote at y= a/b = a/1 or just y=a
what should a be ?

Answer 12

5?

Answer 13

so now we have
(5x + c) / (x+2)

we know that will give us a vertical asymptote at x= - 2 (divide by 0)
and according to the rules you just posted, it will give a horizontal asymptote at y = 5/1 = 5
both of those match your graph.
we still need to figure out what c is ?
I would use the info on the y intercept.

Answer 14

Okay so 7 is the y-intercept

Answer 15

Is that it 5x+7/ x+2 ? @phi

Answer 16

close.

but so far we have

y = (5x+c)/(x+2)
we know when x is 0, y = 7 (definition of y-intercept)
so replace y with 7 and x with 0 in the equation, and solve for c

Answer 17

7=5(0)+c/0+2
7=c/2
c= 14??

Answer 18

yes

Answer 19

Okay so the equation is y=5x+14/x+2

Answer 20

yes, but I would use parens
y = (5x+14)/(x+2)

here is a graph (using geogebra ) of that equation
and it looks like a good match

Answer 21

It does look correct!! although the top 5x+14, do u try to factor that out or just leave as is, cause i think its fine :)

Answer 22

you can't simplify 5x+14
if it were (6x+14) you could write it as 2(3x+7) for example
but 5 and 14 have no common factors.

the answer is just
\[ y = \frac{5x+14}{x+2} \]

Answer 23

Right, oops forgot! now i understand, THANK YOU so much i might be the only kid in the class who can do the reverse AWESOME!!! can't tell u how much i learned :) its great u don't just tell concept but show how to apply it, never would have gotten it without u :D