Find the range of this function h(x)= (3x+2)(x-2)/x(x-2)?

Question

please help..

Answer 1

The function h (x ) = (3x + 2)(x - 2)/x (x - 2)

h (x ) = (3x +2)/x

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

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

y  = (0+2)/0

y = 2/0

In this case no y  intercept .

2) To find x  intercept let the numarator = 0

(3x + 2)

3x = -2

x  = -2/3

x  intercept are -2/3.

3) Vertical asympototes are found  by solving denominator = 0

x = 0

Vertical asympotote is x  = 0 .

4) To find horizontal asymptote.

Degree of the numarator = 1 and the degree of denominator = 1.

If the degree of the numerator is equal to the degree of the denominator,then  horizontal asympotote y = ratio of leading coefficients.

In this case y  = 3 is horizontal asymptote.

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

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

Graph

1) Draw the coordinate plane.

2) Next dash  vertical asympototes.

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

4) Connect the plotted points .

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

 

From the graph range set is the corresponding values of the function for different values of x.

Range = .