The denominator is zero for
= 4. The function is undefined for
Is the function in simplest form?
The numerator and denominator have common factors. Therefore, the rational function is in not in simplest form.
Rewrite in simplest form.
Rewrite the function in simplest form.
Find the vertical asymptote.
The rational expression is in simplest form and is defined for all real values of
. Therefore, the function has no vertical asymptote.
Find the holes in the function.
= 4 is not in the domain of the function. The rational expression in simplest form is defined for
= 4. Therefore, the function has a hole at
= 4. To find the hole in the function, substitute 4 for
– 1 = (4) – 1 or 3
The function has a hole at (4, 3).
Plot the hole.
Plot the hole with an open circle.
Make a table of values.
Substitute values for
= 4 in the function. Find
. Make a table of values.