Write the equation of the transformed graph of tangent with period 6 that has been shifted vertically up 2 units. (3 points)

Question

Write the equation of the transformed graph of tangent with period 6 that has been shifted vertically up 2 units. (3 points)

Answer 1

Note that tan(x) has a period of π (not 2π). Below, this affects the equation for our b coefficient.

y = ±a tan (bx – c) + d

a = amplitude = 1

There is no flipping across the x-axis means start with a = 1

(so there is no a coefficient in our transformed equation)

period = 6 = π/b, so b = π/(period) = π/6

there’s no phase shift, so c = 0

(so there is no c coefficient in our transformed equation)

shifted vertically up 2 units means d = 2

So our required equation is

y = tan ((π/6)x) + 2