The rational function is , where is week of operation.

represents opening.

(a).

Find the domain.

The domain of a  function is the set of all real numbers which makes the function mathematically correct.

Denominator of a function should not be .

Therefore the function is undefined at the real zero of the denominator .

Consider .

Rewrite the equation.

The zeros of the polynomial are and .

Since the car wash cannot be open for the negative weeks and does not fall into the domain.

Therefore, domain is .

(b).

Find the intercepts.

The function is .

Change to .

.

To find intercept, substitute in the function.

intercept is .

To find intercept, subustiute in the function.

intercept is .

Find vertical asymptotes.

Although there are vertical asymptotes at and ,which are not to be considered because the values are not in the domain.

Therefore there are no vertical asymptotes.

Find Horizantal asymptotes. \ \

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

Degree of the numerator and degree of the denominator .  

Since the degree of numerator and degree of denominator are same the horizantal asymptote is the ratio of the variables.

So the function has horizontal asymptote at .

(c).

Graph :

The function is .

Draw the coordinate plane. \ \

Graph the function.

(a). Domain is .

(b). intercept is , intercept is .

No vertical asymptotes.

Horizontal asymptote, at .

(c).

The graph of the function is