Use the graph to determine the domain and the range of the function.

Question

Graph the function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of the function.

y = cot (1/4 x)

Answer 1

Step 1:

The function

Compare it to .

Period.

Find the verticaasymptotes by solving and

and

The two consecutive vertical asymptotes occur at and .

Step 2:

The interval corresponds to two cycle of the graph. Dividing this interval into four equal parts produces the key points.

one fourth of part

The - coordinates of the five key points are

,

Step 3:

Between these two asymptotes, plot a few points as shown in the table.

 

Comments

Step 4:

Graph:

(1) First plot the asymptotes.

(2) The period of the function is the distance between two consecutive vertical asymptotes. The amplitude of a cotangent function is not defined.

(3) plot key points between the two asymptotes and plot another point to sketch two cycles.

Domain is where is an integer.

Range is .

Solution :

Domain is where is an integer.

Range is .