AnswersAlgebra IIGraphing Cosecant and Secant Functions

Graphing Cosecant and Secant Functions — Quiz Answers

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What is the domain of y is equal to cosecant of x ?

A
all real numbers except n pi , where n is any integer
B
all real numbers except n pi plus pi over 2 , where n is any integer
C
all real numbers greater than 1 or less than negative 1
D
all real numbers
2
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What is the range of y is equal to cosecant of x ?

A
y is greater than or equal to 1
B
y is less than or equal to negative 1
C
negative 1 is less than or equal to y comma y is less than or equal to 1
D
y is less than or equal to negative 1 or y is greater than or equal to 1
3

Which of the following is the graph of the function y is equal to 2 point 5 secant open paren x minus 5 close paren ?

A
Image with description 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).
B
Image with description 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).
C
Image with description 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
Image with description 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).
4

What is the domain of y is equal to secant of x ?

A
all real numbers except n pi and n pi plus pi over 2 , where n is any integer
B
all real numbers except n pi , where n is any integer
C
all real numbers
D
all real numbers except n pi plus pi over 2 , where n is any integer
5

The parent secant function is shifted 2 units down, and its period is changed to π Which of the following is the graph of the transformed function?

A
Image with description 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).
B
Image with description 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).
C
Image with description 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).
D
Image with description 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).
6

Which of the following is an asymptote of y is equal to secant of x ?

A
x is equal to 3 pi over 2
B
x is equal to negative pi over 6
C
x is equal to negative 2 pi
D
x is equal to pi
7

Which of the following is an asymptote of y is equal to cosecant of x ?

A
x is equal to negative pi
B
x is equal to negative pi over 3
C
x is equal to pi over 2
D
x is equal to pi over 4
8

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
Image with description 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
Image with description 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).
C
Image with description 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).
D
Image with description 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).
9

What is the period of y is equal to cosecant of x ?

A
4 pi
B
pi
C
3 pi
D
2 pi
10

How is the graph of y is equal to cosecant of open paren x minus 6 close paren transformed from its parent function?

A
It is the graph of y is equal to cosecant of x shifted 6 units up.
B
It is the graph of y is equal to cosecant of x shifted 6 units down.
C
It is the graph of y is equal to cosecant of x shifted 6 units right.
D
It is the graph of y is equal to cosecant of x shifted 6 units left.

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