AnswersSS26 Math 3 S2 M3960OXGraphing Tangent and Cotangent

Graphing Tangent and Cotangent Answers

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What is the range of the function ?

Question illustration
A
all real numbers
B
all real numbers except , where n is any integer
Option B
C
all real numbers except , where n is any integer
Option C
D
all real numbers except , where n is any integer
Option D
2
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Where does the graph of the function have asymptotes?

Question illustration
A
at the values of x where
Option A
B
at the values of x where
Option B
C
at the values of x where is undefined
Option C
D
at the values of x where is undefined
Option D
3

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?

Question illustration
A
He graphed the function incorrectly because he didn’t translate the graph of the parent function 1 unit up.
Option A
B
He graphed the function incorrectly because the period of the transformed function is not units.
Option B
C
He graphed the function correctly, but it was not the right function to graph. He should have graphed .
Option C
D
He graphed the function correctly, but it was not the right function to graph. He should have graphed .
Option D
4

What function is graphed below?

Question illustration
A
y equal to cotangent (StartFraction 3 over 4 EndFraction (x minus StartFraction pi over 6 EndFraction ))
Option A
B
y equal to cotangent (StartFraction 3 over 2 EndFraction (x minus StartFraction pi over 6 EndFraction ))
Option B
C
y equal to cotangent (StartFraction 3 over 4 EndFraction (x plus StartFraction pi over 6 EndFraction ))
Option C
D
y equal to cotangent (StartFraction 3 over 2 EndFraction (x plus StartFraction pi over 6 EndFraction ))
Option D
5

Which function is equivalent to ?

Question illustration
A
y equal to minus tangent (x)
Option A
B
y equal to minus tangent ( x plusStartFraction pi over2 EndFraction)
Option B
C
y equal to tangent (x)
Option C
D
y equal to tangent ( x plusStartFraction pi over2 EndFraction)
Option D
6

What function is graphed below?

Question illustration
A
y equal to cotangent (x minus StartFraction pi over 4 EndFraction)
Option A
B
y equal to tangent (x minus StartFraction pi over 4 EndFraction)
Option B
C
y equal to cotangent (x plus StartFraction pi over 4 EndFraction)
Option C
D
y equal to tangent (x plus StartFraction pi over 4 EndFraction)
Option D
7

What are the x-intercepts of the graph of the function ? Use your graphing calculator to estimate the answer.

Question illustration
A
, where n is any integer
Option A
B
, where n is any integer
Option B
C
, where n is any integer
Option C
D
, where n is any integer
Option D
8

What function is graphed below?

Question illustration
A
y equal to cotangent (x) minus 2
Option A
B
y equal to tangent (x) minus 2
Option B
C
y equal to cotangent (x) plus 2
Option C
D
y equal to tangent (x) plus 2
Option D
9

What is the period of the function ?

Question illustration
A
3 units
B
4 units
C
6 units
D
8 units
10

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?

Question illustration
A
a is less than minus 1
Option A
B
a is greater than minus 1 but less than 0
Option B
C
a is greater than 0 but less than 1
Option C
D
a is greater than 1
Option D

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