What are the period, phase shift, and vertical shift of y is equal to cosecant of open bracket 3 times open paren x plus 4 close paren close bracket plus 6 ?
Answer
A
period: pi over 3 ; phase shift: 4 units left; vertical shift: 6 units down
B
period: 2 pi over 3 ; phase shift: 4 units left; vertical shift: 6 units up
C
period: pi over 3 ; phase shift: 4 units right; vertical shift: 6 units up
D
period: 2 pi over 3 ; phase shift: 4 units right; vertical shift: 6 units down
Explanation
The cosecant function has the same period as sine: 2π divided by the coefficient of x. Here that coefficient is 3, so the period is 2π/3. Since the input is 3(x + 4), the graph shifts 4 units left; the +6 outside shifts it 6 units up. Therefore, the correct choice is A.
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