Question

Use a graphing utility to graph the function. Include two full periods.

y = tan x/3

Answer 1

Step 1:

The trigonometric function is .

Compare the function   with .

and Period = .

Two consecutive vertical asymptotes can be found by solving the equations and .

and

and  .

The two consecutive vertical asymptotes occur at and .

Step 2:

The interval corresponds to one 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

,

,

,

, and

.

Comments

Step 3:

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

Step 4:

Graph:

(1) First plot the asymptotes and the midpoint between two consecutive vertical asymptotes is an - intercept of the graph.

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

(3) After plotting the asymptotes and the - intercept, plot a few additional points between the two asymptotes and sketch one cycle. Finally, sketch one or two additional cycles to the left and right.

(4) Plot these five points and draw the graph of the tangent function.

Solution:

The graph of is :