Graphing Tangent and Cotangent Answers
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1
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Suppose the graph of the parent function is vertically compressed to produce the graph of the function , but there are no reflections. Which describes the value of a?
A
a is less than minus 1B
a is greater than minus 1 but less than 0C
a is greater than 0 but less than 1D
a is greater than 12
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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.
3
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)4
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 .
5
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
6
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
7
Which is the graph of the function ?
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi. The graph increases in every pi interval as x increases. The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi. The graph decreases in every pi interval as x decreases. The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The graph decreases in every pi interval as x decreases.The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The graph increases in every pi interval as x increases. The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).
8
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
9
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
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 ))
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