Graphing Tangent and Cotangent Answers
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1
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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 .
2
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What function is graphed below?
A
y equal to cotangent (x minus StartFraction pi over 4 EndFraction)
B
y equal to tangent (x minus StartFraction pi over 4 EndFraction)
C
y equal to cotangent (x plus StartFraction pi over 4 EndFraction)
D
y equal to tangent (x plus StartFraction pi over 4 EndFraction)
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
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 ))
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 is the period of the function ?
A
3 unitsB
4 unitsC
6 unitsD
8 units7
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
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
9
Where does the graph of the function have asymptotes?
A
at the values of x where
B
at the values of x where
C
at the values of x where is undefined
D
at the values of x where is undefined
10
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).
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