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
Solve x 2 -10 Solution There is a quite simple procedure to solving these.  If you can memorize it you'll always be able to solve these kinds of inequalities. Step 1:

Domain and Range The domain of any equation is the set of all x's which we can plug in the equation & get back a real number for y. The range of any equation is the set of all

It is the final type of problems which we'll be looking at in this section.  We are going to be looking at mixing solutions of distinct percentages to obtain a new percentage. The

Example Solve out the following system of equations. x 2 + y 2  = 10 2 x + y = 1 Solution In linear systems we had the alternative of using either method on any gi

The title of this section is perhaps a little misleading.  The title appears to imply that we're going to look at equations which involve any radicals.  However, we are going to li

Find all the eighth roots of (19 + 7 i)

An artifact was found and tested for its carbon-14 content. If 86% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has