Graphing Cosecant and Secant Functions Answers
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1
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What are the period, phase shift, and vertical shift of y = csc[3(x + 4)] + 6?
A
period: ; phase shift: 4 units right; vertical shift: 6 units up
B
period: ; phase shift: 4 units left; vertical shift: 6 units down
C
period: ; phase shift: 4 units left; vertical shift: 6 units up
D
period: ; phase shift: 4 units right; vertical shift: 6 units down
2
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The parent secant function is shifted 2 units down, and its period is changed to . Which of the following is the graph of the transformed function?
A
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 2 units and the y axis ranges from negative 2 to 4 with an interval of 1 unit. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 3 at (0 comma 3). The graph touches another line y equals 1 at (pi comma 1) and (negative pi comma 1).
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 4 to 2 with an interval of 1 unit. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 3 at (2 pi comma negative 1),(0 comma negative 1) and (negative 2 pi comma negative 1). The graph touches another line y equals negative 3 at (pi comma negative 3) and (negative pi comma negative 3).
C
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi units and the y axis ranges from negative 2 to 4 with an interval of 1 unit. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 3 at (pi comma 3), (0 comma 3) and (negative pi comma 3). The graph touches another line y equals 1 at (pi by 2 comma 1) and (negative pi by 2 comma 1).
D
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi units and the y axis ranges from negative 4 to 2 with an interval of 1 unit. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 1 at (pi comma negative1), (0 comma negative1) and (negative pi comma negative 1). The graph touches another line y equals negative 3 at (pi by 2 comma negative 3) and (negative pi by 2 comma negative 3).
3
What are the period and vertical shift of the cosecant function below?
A
period: ; vertical shift: 1 unit up
B
period: ; vertical shift: 2 units up
C
period: ; vertical shift: 1 unit up
D
period: ; vertical shift: 2 units up
4
What is the range of y = csc(x)?
A
y –1
B
y 1
C
y –1 or y 1
D
–1 y 1
5
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).
6
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).
7
Which of the following is an asymptote of y = sec(x)?
A
x equal to minus 2 pi.
B
x equal to minus StartFraction pi over 6 EndFraction.
C
x equal to pi.
D
x equal to StartFraction 2 pi over 2 EndFraction.
8
What is the domain of y = csc(x)?
A
all real numbersB
all real numbers except , where n is any integer
C
all real numbers except , where is any integer
D
all real numbers greater than 1 or less than –19
What is the period of y = csc(x)?
A
Pi
B
2 pi.
C
3 pi.
D
4 pi.
10
Which of the following is the graph of ?
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 20 with an interval of 4 units. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 5 at (3 by 2 pi comma 5), (pi by 2 comma 5), (negative pi by 2 comma 5) and (negative 3 pi by 2 comma 5). Another line y equals negative 1 touches at (2 pi comma negative 1), (pi comma negative 1), (0 comma negative 1), (negative pi comma negative 1) and (negative 2 pi comma negative 1).
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 20 with an interval of 4 units. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 5 at (9 by 5 pi comma 5), (4 by 5 pi comma 5), (negative 1 by 5 pi comma 5) and (negative 6 by 5 pi comma 5). Another line y equals negative 1 touches at (6 by 5 pi comma negative 1), (1 by 5 pi comma negative 1), (negative 4 by 5 pi comma negative 1) and (negative 9 by 5 pi comma negative 1).
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 12 to 20 with an interval of 4 units. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 5 at (pi comma 5) and (negative pi comma 5). Another line y equals negative 1 touches at (2 pi comma negative 1), (0 comma negative 1) and (negative 2 pi comma negative 1).
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 20 with an interval of 4 units. A secant function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 3 at (pi comma 3) and (negative pi comma 3). Another line y equals negative 3 touches at (2 pi comma negative 3), (0 comma negative 3) and (negative 2 pi comma negative 3).
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