How do you find the amplitude, period, and shift for y=3tanx?

Dec 31, 2017

amplitude: N/A
period: ${180}^{\circ}$
phase shift: $0$

Explanation:

amplitude: how far the graph extends from its midline

e.g. the amplitude of $y = \sin x$ is $1$, since the midline is $y = 0$, and the highest and lowest points are $1$ and $- 1$.

the amplitude of $y = 3 \sin x$ is $3$, since the midline is $y = 0$, and the highest and lowest points are $3$ and $- 3$.

however, the $\tan x$ graph does not have a certain amplitude.

$\tan {90}^{\circ}$ is undefined. without knowing the highest point on the graph, the distance that the graph extends from the midline cannot be calculated.

period: how often the values of the graph repeat themselves

$3 \tan {0}^{\circ} = 0 , 3 \tan {180}^{\circ} = 0$

$3 \tan {45}^{\circ} = 3 , 3 \tan {225}^{\circ} = 3$

${180}^{\circ} - {0}^{\circ} = {180}^{\circ}$
${225}^{\circ} - {45}^{\circ} = {180}^{\circ}$

this means that the values of $\tan {x}^{\circ}$ on the graph recur every ${180}^{\circ}$.

phase shift: how far to the right a wave is from its usual position.

usual position of $y = \tan x$:

graph{tan x [-10, 10, -5, 5]}

$y = 3 \tan x$:

graph{3tan x [-10, 10, -5, 5]}

the graph has not been moved in either horizontal direction - the values for both at $x = 0$ are both the same.