Question

Graph two periods of the given tangent function. y = tan(x − π/4)

Accepted Answer

Identify the basic form of the tangent function given: $$y = 	an(x - \frac{\pi}{4}). $$This is a horizontal shift of the standard tangent function $$y = 	an x by$$ $$\frac{\pi}{4}$$ units to the right. Recall that the tangent function has a period of $$\pi. $$Since the problem asks for two periods, determine the interval length to graph: $$2 	imes \pi = 2\pi. $$Find the new domain interval for two periods considering the phase shift. Since the function is shifted right by $$\frac{\pi}{4}$$, the interval for two periods can be from $$x = \frac{\pi}{4} to$$ $$x = \frac{\pi}{4} + 2\pi. $$Identify the vertical asymptotes of the function. For $$y = 	an(x - \frac{\pi}{4})$$, asymptotes occur where the argument of tangent is $$\frac{\pi}{2} + k\pi$$, so solve $$x - \frac{\pi}{4} = \frac{\pi}{2} + k\pi$$ for $$x to $$find asymptotes within the interval. Plot key points between asymptotes by evaluating $$y = 	an(x - \frac{\pi}{4}) at $$values such as the midpoints between asymptotes, then sketch the curve showing the characteristic shape of the tangent function over two periods.

Graph two periods of the given tangent function. y = tan(x − π/4)

Verified video answer for a similar problem:

Key Concepts

Period of the Tangent Function

Horizontal Phase Shift

Asymptotes of the Tangent Function