Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\(y = \frac{1}{4}tan\left( {x - \frac{\pi }{4}} \right)\)

Short answer

The plot of the function \(y = \frac{1}{4}tan\left( {x - \frac{\pi }{4}} \right)\) is:

Step-by-step solution

Given data

The function to be plotted is \(y = \frac{1}{4}\tan \left( {x - \frac{\pi }{4}} \right)\).

Plot of the function \(y = tanx\)

The plot of the function \(y = \tan x\) is as follows

Plot of the function \(y = \frac{1}{4}tan\left( {x - \frac{\pi }{4}} \right)\)

The plot of the function \(y = \tan \left( {x - \frac{\pi }{4}} \right)\) can be obtained by shifting Figure 1 to the right by \(\frac{\pi }{4}\) as follows:

The plot of the function \(y = \frac{1}{4}{\rm{tan}}\left( {x - \frac{\pi }{4}} \right)\) can be obtained by scaling down Figure 2 by 4. The plot will become more curved without changing the points where \(y = 0\) and \(y \to \infty \) as follows: