Where online can i find something that graphs intervals for you?

Question

This is what I have to do.

1. Draw the graph of a rational function that is positive for x < 2 and negative for x > 2 on the coordinate plane below.

&

2. Draw the graph of a rational function that is increasing for x < –4 and decreasing for x > –4 on the coordinate plane below.

Answer 1

1) The general form of rational function f(x) = N(x) / D(x) where N(x) and D(x) are polynomials.

y = N(x) / D(x)

In this case

x < 2 , rational function is positive.

Therfore x < 2 ⇒ y is positive.

x > 2 , rational function is negative.

Therfore x > 2 ⇒ y is negitive.

Vertical asympotote x  = 2, horizontal asymptote y  =  0 .

Vertical asympototes of rational function are found by D(x) = 0

Therfore the denominator is x - 2.

D(x) = x - 2

Next find the polynomial N(x) :

If the degree of the numarator is less than degree of the denominator  there is horizontal asympotote y = 0, which say x axis.

numarator degree is 0.

Possible numarator is N(x) = x ^0 (-1)

N(x) is - 1

So far we have the rational function f(x) = - 1 / (x - 2)

Therfore the rational function f(x) = - 1 / (x - 2)

Graph

The graph of rational functions can be recognised by the fact two or more parts.

 y = - 1 / (x - 2)

To find  y intercept  x = 0 in the rational function.

y = -1/(0 - 2)

In this case y  intercept is 0.5 .

In this case there is no x  intercept.

Now i will pick few more x - values, compute the corresponding y  values and flat few more points.

x	y = -1 / (x - 2)	(x , y )
- 1	y = -1 / (-1 -2) = 1/3	(-1,1/3)
- 3	y = -1 / (-3 -2) = 1/5	(-3 , 1/5)
1	y  = -1 / (1 - 2) = 1	(1,1)
3	y = -1 / (3 -2) = -1	(3,-1)
4	y = -1 / (4 -2) = -1/2	(4,-1/2)

1) Draw the coordinate plane.

2) Next dash the horizontal and vertical asympototes

3) Plot the y intercept and coordinate pairs found in the table..

4) Connect the plotted points .

When you draw your graph, use smmoth curves complete the graph.