Graphing Tangent and Cotangent Answers
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1
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What is the period of y = csc(x)?
A
Pi
B
2 pi.
C
3 pi.
D
4 pi.
2
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Which of the following is the graph of the function y = 2.5sec(x – 5)?
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 4 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 7 point 8 at (2 pi comma 7 point 8) and (negative 2 pi comma 7 point 8) and y equals 2 at ( pi comma 2) and (negative pi comma 2).
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 4 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 4 at (2 pi comma negative 4), (0 comma negative 4) and (negative pi comma negative 4) and y equals negative 6 at ( pi comma negative 6) and (negative pi comma negative 6).
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 8 to 8 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 2 at (3 by 2 pi comma 2) and (negative pi by 2 comma 2) and y equals negative 2 at (5 by 2 pi comma negative 2) and ( pi by 2 comma negative 2).
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 12 to 12 with an interval of 4 units. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals 5 at (4 by 5 pi comma 5) and (14 by 5 pi comma 5) and y equals negative 5 at (9 by 5 pi comma negative 5) and (negative pi by 5 comma negative 5).
3
The parent cosecant function is shifted 4 units right and 3 units up. Which of the following is the graph of the transformed function?
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 7 to 1 with an interval of 1 unit. A cosecant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 2 at (9 by 5 pi comma negative 2) and (negative pi by 5 comma negative 2). The graph touches another line y equals negative 4 at (4 by 5 pi comma negative 4) and (negative 6 by 5 comma negative 4).
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 1 to 7 with an interval of 1 unit. A cosecant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 4 at (9 by 5 pi comma 4) and (negative pi by 5 comma 4). The graph touches another line y equals 2 at (4 by 5 pi comma 2) and (negative 6 by 5 pi comma 2).
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 2 to 6 with an interval of 1 unit. A cosecant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 4 at (4 by 5 pi comma 4) and (negative 6 by 5 pi comma 4). The graph touches another line y equals 2 at (9 by 5 pi comma 2) and (negative 1 by 5 pi comma 2).
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 7 to 1 with an interval of 1 unit. A cosecant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 2 at (4 by 5 pi comma negative 2) and (negative 6 by 5 pi comma negative 2). The graph touches another line y equals negative 4 at (9 by 5 pi comma negative 4) and (negative 1 by 5 pi comma negative 4).
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