Question

39-40 Locate the discontinuities of the function and illustrate by graphing.

\(y = {\bf{arctan}}\frac{{\bf{1}}}{x}\)

Short answer

The function is discontinuous at \(x = 0\).

Step-by-step solution

Find the point of discontinuity

The function \(\frac{1}{x}\) is not defined at \(x = 0\).

So, the function y is discontinuous at \(x = 0\).

Sketch the graph of y

Use the following steps to plot the graph of given functions:

1) In the graphing calculator, select “STAT PLOT” and enter the equation \(\arctan \frac{1}{X}\) in the \({Y_1}\) tab.

2) Enter the graph button in the graphing calculator.

The figure below represents the graph of \(y = \arctan \frac{1}{x}\).

Thus, the graph is obtained.