Sketch the graph of function, Algebra

Sketch the graph of function.

f ( x ) =3x + 6 /x -1


Thus, we'll start off with the intercepts. The y-intercept is,

      f (0) =6/-1=-6⇒     (0, -6)


The x-intercepts will be,

3x + 6 = 0

x = -2                   ⇒ ( -2, 0)

Now, we have to determine the asymptotes.  Let's first determine the vertical asymptotes.

x -1 =0                 ⇒   x = 1

Thus, we've got one vertical asymptote. It means that now there are two regions of x's. They are x < 1 and x > 1 .

Now, the largest exponent within the numerator & denominator is 1 and thus by the fact there will be a horizontal asymptote at the line.

                                                   y = 3/1 = 3

Now, we only need points in each region of x's.  As the y-intercept & x-intercept are already in the left region we won't have to get any points there.  It means that we'll only need to get a point in the right region.  It doesn't actually matter what value of x we pick here we only have to keep it rather small so it will fit onto our graph.

f ( 2) = 3( 2) + 6/2 -1 = 12 /1= 12   ⇒  ( 2,12)

Putting all this together illustrate the following graph.

1639_Sketch the graph of function.png

Posted Date: 4/8/2013 2:11:36 AM | Location : United States

Related Discussions:- Sketch the graph of function, Assignment Help, Ask Question on Sketch the graph of function, Get Answer, Expert's Help, Sketch the graph of function Discussions

Write discussion on Sketch the graph of function
Your posts are moderated
Related Questions
I have an algebra test tomorrow and still don''t understand how to simplify and solve radicals

Now we need to discuss graphing functions. If we recall from the earlier section we said that f ( x ) is nothing more than a fancy way of writing y. It means that already we kno

Now, we've got some terminology to get out of the way. Multiplicity k  If r is a zero of a polynomial and the exponent on the term that produced the root is k then we say t

linear functions

There are two forms of the parabola which we will be looking at. The first form will make graphing parabolas very simple.  Unluckily, most parabolas are not in this form.  The seco

Coordinates for the point  The listed first number is the x-coordinate of the point and the second number listed is the y-coordinate of the point. The ordered pair for any spec

x+y=6 -x+y=-6 how do I write that in order to graph it?

How do you simplfly 25 and 15 if u say 5 and the teacher thinks it''s wrong?

what is 500 times 70

The given fact will relate all of these ideas to the multiplicity of the zero. Fact If x = r is a zero of the polynomial P (x) along with multiplicity k then, 1.   If th