Graphing Cosecant and Secant Functions Answers
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1
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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).
2
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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 2 to 2 with an interval of 1 unit. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (pi by 2 comma 1) and (negative 3 by 2 pi comma 1). Another line y equals negative 1 touches at (3 by 2 pi comma negative 1) and (negative pi by 2 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 1 to 3 with an interval of 1 unit. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 point 2 5 at (pi by 2 comma 1 point 2 5) and (negative 3 by 2 pi comma 1 point 2 5). Another line y equals 0 point 7 5 touches at (3 by 2 pi comma 0 point 7 5) and (negative pi by 2 comma 0 point 7 5).
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 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 0 at (pi by 2 comma 0) and (negative 3 by 2 pi comma 0). Another line y equals negative 2 touches at (3 by 2 pi comma negative 2) and (negative 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 1 to 3 with an interval of 1 unit. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 point 2 5 at (3 by 2 pi comma 1 point 2 5) and (negative pi by 2 comma 1 point 2 5). Another line y equals 0 point 7 5 touches at (pi by 2 comma 0 point 7 5) and (negative 3 by 2 pi comma 0 point 7 5).
3
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
4
What is the equation of the graph below?
A
y = sec(x – 4)B
y = sec(x) – 4C
y = sec(x + 4) + 4D
y = sec(x + 4) – 45
How is the graph of y = csc(x – 6) transformed from its parent function?
A
It is the graph of y = csc(x) shifted 6 units up.B
It is the graph of y = csc(x) shifted 6 units right.C
It is the graph of y = csc(x) shifted 6 units left.D
It is the graph of y = csc(x) shifted 6 units down.6
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).
7
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 –18
What is the range of y = csc(x)?
A
y –1
B
y 1
C
y –1 or y 1
D
–1 y 1
9
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
10
What is the period of the cosecant function graphed below?
A
Pi over 2.
B
Pi
C
3 pi over 2.
D
2 pi.
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