Sketching of \(y=a\tan \left( bx \right)\)

y=tan x Tangent has no amplitude, maximum or minimum. Its range is all real numbers. **Function** | **0 (0)** | **90 ((pi)/(2))** | **180 (pi)** | **270 ((3pi)/(2))** | **360 (2pi)** tan x | 0 | Undefined | 0 | Undefined | 0 y=atan(bx), a,b>0 T= 180 b or b Zeros: x= kpib: x= pi2+kpib (k in Z) **Equation** | **Midline** | **Amplitude** | **Maximum and minimum** | **Period** y=3tan 2x-1 | y=-1 | None | None | 90 or (pi)/(2) **Function** | **Period (degrees)** | **Period (radians)** y=5tan 3x | 60 | (pi)/(3) y=3tan 2x | 90 | (pi)/(2) y=tan(3x)/(4) | 240 | (4pi)/(3) y=tan(pi x) | (180)/(pi) | 1 Draw dashed vertical asymptotes, mark the zeros midway between them, then sketch an increasing branch in each interval. Branches never cross vertical asymptotes. Example: y=tan(32x), 0 <= x 2pi Period 2pi3. Zeros: 0, 2pi3, 4pi3,2pi. Vertical asymptotes: 3,pi, 5pi3. Each branch increases between its asymptotes.