Retaining tangent asymptotes

Retaining tangent asymptotes

5 marks

TGM Original

Sketch y=|2tan x+2| for 0 <= x <= pi, omitting undefined inputs. Label zeros and vertical asymptotes. State the reflected portions and range.

Solution:

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Answer:Zero \(\dfrac{3\pi}{4}\); endpoint heights \(2\); asymptote \(x=\dfrac{\pi}{2}\); reflect \(\dfrac{\pi}{2}<x<\dfrac{3\pi}{4}\); range \([0,\infty)\).

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