Question

can anyone help me write an equation of a transformed graph of tangent with period 4 that has been shifted vertically up 3 units

Answer 1

Atan( Bx + C ) + D

D = vertical shift, D > 0, up, D < 0, down

B = parent function's original period change by \(\bf \cfrac{\text{original period}}{B}\)
tangent's original period is \(\bf \large \pi\)

Answer 2

so the equation would be....

Answer 3

tan(4x)+3?

Answer 4

well, you want the original period to change to 4
that means you want \(\bf \cfrac{\text{original period}}{B} = 4 \implies \cfrac{\pi}{B}=4\)

so solve for "B" to see which B you can use to make the period to 4

Answer 5

the +3 part is ok, yes, that'd shift it upwards by 3 units

Answer 6

than is it 1/4?

Answer 7

yes well, pi/4 that is \(\bf \cfrac{\pi}{B}=4 \implies B = \cfrac{\pi}{4}\\
tan\left(\cfrac{\pi}{4}x\right)+3\)