Question

solve the inequality by using the graph of the function.

Answer 1

Step 1:

The rational inequality is , where the rational function .

The graph of a rational function will never intersect a vertical asymptote.

The rational function is .

Find the - intercept by substituting in the rational function.

.

There is no - intercept for the rational function.

Step 2 :

Find the - intercept by substituting in the rational function.

The - intercept is .

Step 3 :

Vertical asymptote can be found by making denominator is equals to zero.

Vertical asymptotes are .

Step 4 :

To find the horizontal asymptote, first find the degree of the numerator and the degree of denominator.

Degree of the numerator = 1 and the degree of denominator = 2.

Since the degree of the numerator is less than the degree of the denominator, is the horizontal asymptote.

is the horizontal asymptote.

Comments

Step 5 :

Need some more points to more accurate graph.

Choose random values for and find the corresponding values for .

Step 6 :

Graph :

1) Draw the coordinate plane.

2) Next dash the horizontal and vertical asymptotes

3) Plot the , intercepts and coordinate pairs found in the table..

4) Connect the plotted points with smooth curves

Step 7 :

First determine the intervals of such that the graph is above the - axis from the graph.

From the graph, observe that, for .

The solution set is .

Solution :

The solution set is .