Write the equation of the curve in its final position: the graph of y = tan (x) is shifted by (pi/6) units to the right, stretched by a factor of 3, then translated 8 units up.
y = tan[3[x-II/6]+8
To find the equation of the curve in its final position, we need to apply the given transformations to the original equation of the curve y = tan(x). Let's break down the transformations step by step:
1. Shift π/6 units to the right:
To shift the graph to the right, we subtract π/6 from x. Therefore, the new equation becomes y = tan(x - π/6).
2. Stretch by a factor of 3:
To stretch the graph vertically, we multiply the y-values by 3. The equation now becomes y = 3tan(x - π/6).
3. Translate 8 units up:
To translate the graph vertically, we add 8 to the y-values. The final equation is y = 3tan(x - π/6) + 8.
So, the equation of the curve in its final position is y = 3tan(x - π/6) + 8.