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
.