Question

The graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y= -tan x, y = −tan(x − π/2).

Accepted Answer

Identify the vertical asymptotes of the tangent graph. From the graph, the asymptotes are at $$x = -\frac{3\pi}{4}$$ and $$x = \frac{\pi}{4}. $$Recall that the standard tangent function $$y = 	an x$$ has vertical asymptotes at $$x = \pm \frac{\pi}{2}$$, and the period is $$\pi. $$The asymptotes in the given graph are shifted horizontally compared to the standard tangent function. Determine the horizontal shift by comparing the asymptotes of the given graph to those of $$y = 	an x. $$The asymptotes of $$y = 	an x$$ are at $$x = \pm \frac{\pi}{2}$$, but here they are at $$x = -\frac{3\pi}{4}$$ and $$x = \frac{\pi}{4}. $$This indicates a shift of $$-\frac{\pi}{4} to $$the left. Use the horizontal shift to write the equation of the tangent function. A shift to the left by $$\frac{\pi}{4}$$ means the function is $$y = 	an\left(x + \frac{\pi}{4}ight). $$However, this is not one of the options, so check if the function is reflected or shifted further. Check the zeros of the function at $$x = -\frac{\pi}{4}$$ and $$x = \frac{3\pi}{4}$$, and compare with the options. By analyzing the behavior and the given options, conclude which equation matches the graph based on the shifts and reflections.

The graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y= -tan x, y = −tan(x − π/2).

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Tangent Function and Its Graph

Horizontal Shifts of Trigonometric Functions

Reflection of the Tangent Function