Question

Find the domain and sketch the graph of the function.

Answer 1

Step 1:

The function is .

The domain of the function is set of all values at which the function is continuous.

The denominator should not be equal to 0.

Thus, the function is continuous for all real numbers except 2.

Domain of the function is

Step 2:

Graph of the function :

Rewrite the above equation:

Factorize the numerator by using  .

Cancel the common terms.

Select values from the domain and make a table.

t
0
1

Graph:

1) Draw the coordinate plane.

2) Plot the points of two lines.

3) Connect the plotted points.

Solution:

Domain of the function is .