Ok, we've been graphing rational functions for about a week now and i've been able to do most of it... until now
Past functions have been factorable or divisble with long division.
But the new problems are different.
ex. y=(x^4-3x^3+x^2-3x+3) / (x^2-3x)
another one is
ex. y=(2x^5-x^3+2) / (x^3-1)
They don't factor and i've tried dividing both with long division and synthetic.
I might just be dumb and dividing wrong but I dont see how it works.
If you could just show me how to do it I would be grateful =)
You can use long division on both problems. You might have a remainder, but you can still do it.
For the first problem you begin with
goes into times. So you subtract from , which is:
Save the factor of for the quotient.
Now, goes into once, so you subtract from , which gives you 3.
So your quotient is with a remainder of 3, or exactly .
Ok, so I divided the first one and got x^2+1 (we're supposed to drop the remainder), but I still don't see how that fits into graphing it?
So would the Root be x=-1?
We have to find the Roots/holes, the Vertical Asymptotes, the Horizontal Asymptotes, and the Y-intercept.
On previous problems they were like so: (x+3)(x-1)(x+2) / (x+2)(x+1)
So I could find the Roots/holes to be x=-3, -2 and 1
But I'm not getting anything close to that on these :/
has no real roots.
Also, a root and a "hole" are different things.
For the equation
the roots are -3 and 1, and the "holes" occur at x = -1 and x = -2. -2 is not a root because the function is not defined there.
A vertical asymptote occurs wherever there is a "hole".
We'll, she says as x goes farther away, the remainder gets closer and closer to 0 so we're just supposed to drop it.
And what we're supposed to do is draw a graph grid and put in the roots and holes and the x axis and draw dotted lines going up and down for the asymptotes and put in the y-intercept and pretty much just connect the dots without crossing a vertical asymptote.
And there is no y-intercept in this problem so we would have to pick an x value and plug it in to get a y value for an extra point.
What my question is, is I get but I don't know what it means. :/ Get what i'm saying?
Like what exactly is that number?
Is it the simplified equation or just the top part?
This means that the entire function is an asymptote.
Originally Posted by cheet0face