Question

What are the period and phase shift for f(x) = 3 tan(4x + π)?

Answer 1

`\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ \end{array}`





`\bf \begin{array}{llll} \bullet \textit{vertical shift by }{{ D}}\\ \qquad if\ {{ D}}\textit{ is negative, downwards}\\ \qquad if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period}\\ \qquad \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\ \qquad \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta) \end{array}`


now.. with that template above in mind, let's see yours



`\bf \begin{array}{lllllll} f(x)=&3tan(&4x+&\pi )\\ f(x)=&3tan(&4x+&1\pi )&+0\\ &\uparrow &\uparrow &\uparrow &\uparrow \\ &A&B&C&D \end{array}`