Graphing Tangent and Cotangent Answers
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1
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What transformations were applied to the graph of the parent function to produce the function graphed below?
A
a horizontal compression to produce a period of and a horizontal translation of units to the left
B
a horizontal compression to produce a period of and a horizontal translation of units to the right
C
a horizontal stretch to produce a period of and a horizontal translation of units to the left
D
a horizontal stretch to produce a period of and a horizontal translation of units to the right
2
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Chris wanted to transform the graph of the parent function by horizontally compressing it so that it has a period of units, horizontally translating it units to the right, and vertically translating it 1 unit up. To do so, he graphed the function , as shown. What did he do wrong?
A
He graphed the function incorrectly because he didn’t translate the graph of the parent function 1 unit up.
B
He graphed the function incorrectly because the period of the transformed function is not units.
C
He graphed the function correctly, but it was not the right function to graph. He should have graphed .
D
He graphed the function correctly, but it was not the right function to graph. He should have graphed .
3
What is the period of the function ?
A
3 unitsB
4 unitsC
6 unitsD
8 units4
What function is graphed below?
A
y equal to cotangent (x) minus 2
B
y equal to tangent (x) minus 2
C
y equal to cotangent (x) plus 2
D
y equal to tangent (x) plus 2
5
What is the range of the function ?
A
all real numbersB
all real numbers except , where n is any integer
C
all real numbers except , where n is any integer
D
all real numbers except , where n is any integer
6
Eve’s teacher asked her to graph the function by reflecting the graph of the function about the x-axis and translating it vertically. Does it matter in which order Eve does the transformations?
A
Yes, it matters. The graph of the function should be reflected about the x-axis before it is translated 1 unit down.
B
Yes, it matters. The graph of the function should be reflected about the x-axis before it is translated 1 unit up.
C
No, it doesn’t matter. Reflecting the graph of the function about the x-axis and translating the graph 1 unit down in either order will produce the correct graph.
D
No, it doesn’t matter. Reflecting the graph of the function about the x-axis and translating the graph 1 unit up in either order will produce the correct graph.
7
Which is an asymptote of the graph of the function ?
A
x equal to minus StartFraction 4pi over 3 EndFraction
B
x equal to minus StartFraction 2 pi over 3 EndFraction
C
x equal to StartFraction 3 pi over 4 EndFraction
D
x equal to StartFraction 3pi over 2 EndFraction
8
Which function is equivalent to ?
A
y equal to minus tangent (x)B
y equal to minus tangent ( x plusStartFraction pi over2 EndFraction)C
y equal to tangent (x)D
y equal to tangent ( x plusStartFraction pi over2 EndFraction)9
Which is an asymptote of the graph of the function ?
A
mc020-2.jpg
B
mc020-3.jpg
C
mc020-4.jpg
D
mc020-5.jpg
10
What function is graphed below?
A
y equal to cotangent (StartFraction 3 over 4 EndFraction (x minus StartFraction pi over 6 EndFraction ))
B
y equal to cotangent (StartFraction 3 over 2 EndFraction (x minus StartFraction pi over 6 EndFraction ))
C
y equal to cotangent (StartFraction 3 over 4 EndFraction (x plus StartFraction pi over 6 EndFraction ))
D
y equal to cotangent (StartFraction 3 over 2 EndFraction (x plus StartFraction pi over 6 EndFraction ))
11
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).
12
Which of the following is an asymptote of y = csc(x)?
A
x equal to minus pi.
B
x equal to minus StartFraction pi over 3 EndFraction.
C
x equal to StartFraction pi over 4 EndFraction.
D
x equal to StartFraction pi over 2 EndFraction.
13
What is the range of y = csc(x)?
A
y –1
B
y 1
C
y –1 or y 1
D
–1 y 1
14
What is the period of y = csc(x)?
A
Pi
B
2 pi.
C
3 pi.
D
4 pi.
15
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.
16
What is the domain of y = sec(x)?
A
all real numbersB
all real numbers except , where n is any integer
C
all real numbers except , where n is any integer
D
all real numbers except and , where n is any integer
17
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 –118
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.19
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).
20
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) – 4Did you find these answers helpful?
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