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
A toy manufacturer develops a formula to determine the demand for its product depending on the price in dollars. The formula is , where P is the price per unit and D is the number

Example: Solve following equations. 2 log 9 (√x) - log 9 (6x -1) = 0 Solution  Along with this equation there are two logarithms only in the equation thus it's easy t

need step by step instructions on solving P = $500 and r = 11% = .11

square root of j+ square root of j +14 = 3 square root j +10. what is the value of J?

What would an equation of this line passing through each pair of points given?

Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition. Given two functions

What is 789673+469767 equal to?

As a fundraiser a school is selling posters.The printer charges a $24 set up fee plus 0.20 for each poster. Then the cost y in dollars to print is given by the linear equation y=0.