Question
How do I find the vertical asymptotes for y=-2tan((3x+180°)+3) without graphing?
Answers
Steve
recall your knowledge of transformations.
tan(x) has period π, with asymptotes as π/2 + nπ
That means that
tan(kx) has period π/k with asymptotes at (π/2+nπ)/k = π/2k + n*π/k
Now, (3x+180)=3(x+60)
so, the graph has been shifted left by π/3 and has period π/3
So, it has asymptotes at (π/2+nπ)/3-π/3 = π/6+n*π/3
the scale factor and vertical shift do not affect the vertical asymptotes.
tan(x) has period π, with asymptotes as π/2 + nπ
That means that
tan(kx) has period π/k with asymptotes at (π/2+nπ)/k = π/2k + n*π/k
Now, (3x+180)=3(x+60)
so, the graph has been shifted left by π/3 and has period π/3
So, it has asymptotes at (π/2+nπ)/3-π/3 = π/6+n*π/3
the scale factor and vertical shift do not affect the vertical asymptotes.