[tex]undefined[/tex]
Explanation:
[tex]f(x)\text{ = 4tan(2x + }\frac{\pi}{3})[/tex][tex]\begin{gathered} \text{trigonometry function: STEP 1} \\ y\text{ = Atan(Bx }-\text{ C) + D} \\ A\text{ = 4} \\ B\text{ = 2} \\ -C\text{ = }\frac{\pi}{3} \\ C\text{ =- }\frac{\pi}{3} \\ D\text{ = 0} \\ y\text{ = 4tan\lbrack{}2x }-\text{ (- }\frac{\pi}{3}\text{)\rbrack + 0} \end{gathered}[/tex][tex]\begin{gathered} \text{STEP 2:} \\ |A|\text{ = }|4| \\ \text{Stretching /compressing factor = |A| = 4} \end{gathered}[/tex][tex]\begin{gathered} \text{STEP 3} \\ \text{period P = }\frac{\pi}{|B|}\text{ } \\ \text{P = }\frac{\pi}{|2|} \\ P\text{ = }\frac{\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{STEP 4} \\ \text{Horizontal shift x = }\frac{C}{B} \\ x\text{ = }\frac{-\pi}{3}\text{ }\div\text{ }2 \\ x\text{ = }\frac{-\pi}{3}\times\text{ }\frac{1}{2} \\ x\text{ = }\frac{-\pi}{6} \end{gathered}[/tex][tex]\begin{gathered} \text{STEP 5} \\ \text{Vertical shift D = 0} \\ \text{midline equation:} \\ \text{Midline is the vertical shift} \\ \text{Vertical shift = 0} \\ \text{Midline = 0} \end{gathered}[/tex]
