Inverse of a Function — Unit test Answers
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1
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What is the exact value of sin(105°)?
A
Negative StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
B
Negative StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
C
StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
D
StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
2
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What is the value of 1 − 2sin2(105°)?
A
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
B
Negative one-half
C
One-half
D
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
3
Which is the graph of ?
A
A smooth curve resembling an arctangent function. The x-axis ranges from -6 to 6, and the y-axis from -p to p. The curve approaches horizontal asymptotes at y = p/2 and y = -p/2, passing through the origin.
B
A graph of a function with asymptotic behavior. The x-axis ranges from -5 to 5, and the y-axis ranges from -p to p. The curve is located in the fourth quadrant, approaching the y-axis asymptotically as x approaches zero from both positive and negative directions. The curve also approaches zero asymptotically as x moves away from zero in both directions. The function does not intersect either axis.
C
A graph of a function with the x-axis ranging from -2.5 to 2.5 and the y-axis ranging from -p to p. The curve passes through the origin (0,0) and changes direction at y=0. It intersects the x-axis at two points, approximately at x=-1 and x=1. The curve is symmetric about the origin.
D
The image shows a mathematical graph plotted on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -p to p. A smooth, continuous curve intersects the x-axis at approximately 1. The curve extends into both the positive and negative quadrants. The point p is labeled on the positive y-axis and -p on the negative y-axis.
4
For , which expression is equivalent to ?
A
StartFraction 1 Over StartRoot 2 (1 + cosine x) EndRoot EndFraction
B
StartFraction 1 Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction
C
(StartRoot StartFraction 1 + cosine (x) Over 2 EndFraction EndRoot) (StartFraction 1 Over 1 minus cosine (x) EndFraction)
D
(StartFraction 1 + cosine (x) Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction) (StartFraction 1 Over 1 minus cosine (x) EndFraction)
5
What is the exact value of tan(195°)?
A
StartFraction StartRoot 3 EndRoot + 1 Over 1 minus StartRoot 3 EndRoot EndFraction
B
StartFraction StartRoot 3 EndRoot minus 3 Over 3 + StartRoot 3 EndRoot EndFraction
C
StartFraction StartRoot 3 EndRoot minus 1 Over 1 + StartRoot 3 EndRoot EndFraction
D
StartFraction StartRoot 3 EndRoot + 3 Over 3 minus StartRoot 3 EndRoot EndFraction
6
Which expression is equivalent to ?
A
Cosine (negative StartFraction pi Over 3 EndFraction)
B
Sine (negative StartFraction pi Over 3 EndFraction)
C
Cosine (StartFraction pi Over 2 EndFraction)
D
Sine (StartFraction pi Over 2 EndFraction)
7
Which expression is equivalent to ?
A
tan(x)B
–tan(x)C
StartFraction 1 Over cosine (x) EndFraction
D
Negative StartFraction 1 Over cosine (x) EndFraction
8
Review the proof of cos(A - B) = cosAcosB + sinAsinB.Step 1: Step 2: Step 3: Step 4: Step 5:Step 6:Step 7:
A
1 and 1B
2 and 1C
(cosAcosB)2(sinAsinB)2 and (cos2(A – B))((sin2(A – B))D
(cos2A + sin2A)(cos2B + sin2B) and (cos2(A – B))(sin2(A – B))9
Which statement is true about the graph of the equation ?
A
There is a horizontal asymptote at .
B
There is a horizontal asymptote at .
C
There is a vertical asymptote at .
D
There is a vertical asymptote at .
10
Which function is equivalent to the inverse of ?
A
mc020-2.jpg
B
mc020-3.jpg
C
mc020-4.jpg
D
mc020-5.jpg
11
Review the diagram of the unit circle.
A
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus 1) squared minus (sine (u) minus 0) squared EndRoot
B
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (negative v) minus 1) squared + (sine (negative v) minus 0) squared EndRoot
C
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus cosine (negative v) ) squared + (sine (u) minus sine (negative v)) squared
D
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u + v) minus cosine (u) ) squared + (sine (u + v) minus sine (u)) squared EndRoot
12
Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?
A
30° onlyB
90° onlyC
30° or 150°D
30°, 90°, or 150°13
What is the exact value of tan ?
A
Negative 2 minus StartRoot 3 EndRoot
B
Negative 2 + StartRoot 3 EndRoot
C
1 minus StartRoot 3 EndRoot
D
1 + StartRoot 3 EndRoot
14
Which shows a correct simplification of sin(x + )?
A
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · 1 + cos(x) · 0= sin(x)B
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · 1 – sin(x) · 0= cos(x)C
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · –1 + cos(x) · 0= –sin(x)D
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · –1 – sin(x) · 0= –cos(x)15
What are the solutions to the equation over the interval [0, 2]?
A
only
B
only
C
only
D
StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 7 pi Over 6 EndFraction and StartFraction 11 pi Over 6 EndFraction
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