Answers2026-2027_MDCPS_1200330_Algebra 2_FYTransformations of Functions

Transformations of Functions — Unit test Answers

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1
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What are the exact values of the six trigonometric functions for radians?

Question illustration
A
sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; secant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option A
B
sine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot
Option B
C
sine (Negative StartFraction 7 pi Over 6 EndFraction) = one-half; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = 2; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartRoot 3 EndRoot
Option C
D
sine (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction; cosine (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction; tangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot. Cosecant (Negative StartFraction 7 pi Over 6 EndFraction) = StartRoot 3 EndRoot; secant (Negative StartFraction 7 pi Over 6 EndFraction) = Negative StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction; Cotangent (Negative StartFraction 7 pi Over 6 EndFraction) = StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option D
2
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Which of the following are in correct order from greatest to least?

A
, 330°, , ,
Option A
B
, , , , 330°
Option B
C
, , , , 330°
Option C
D
330°, , , ,
Option D
3

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option D
4

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.

A
d = negative 3.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 5
Option A
B
d = negative 3.75 cosine (StartFraction 4 pi Over 29 EndFraction t) + 5
Option B
C
d = negative 2.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 6
Option C
D
d = negative 2.75 cosine (StartFraction 4 pi Over 29 EndFraction t) + 6
Option D
5

How long is the arc intersected by a central angle of radians in a circle with a radius of 6 ft? Round your answer to the nearest tenth. Use 3.14 for .

Question illustration
A
1.0 ft
B
5.7 ft
C
6.3 ft
D
7.0 ft
6

Which measure is of an angle that is coterminal with a 95° angle?

A
95° – (1,450n)°, for any integer n
B
95° – (1,080n)°, for any integer n
C
95° – (780n)°, for any integer n
D
95° – (340n)°, for any integer n
7

Which transformations are needed to change the parent sine function to the sine function below?

Question illustration
A
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left
Option A
B
vertical stretch of 2, horizontal compression to a period of , vertical shift of 2 units up, phase shift of units left
Option B
C
vertical stretch of , horizontal compression to a period of , vertical shift of 1 unit up, phase shift of units left
Option C
D
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit down, phase shift of units left
Option D
8

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

a
absolute value
e
exponential
c
cube root
s
square root
9

Melanie simplified the expression as shown below.Step 1:Step 2:Step 3:Step 4:In which step did Melanie make the first error, and which expression should she have written in that step?

Question illustration
A
step 1;
Option A
B
step 1;
Option B
C
step 4; cos(x)
D
step 4; csc(x)
10

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . What is the height of the ball at its equilibrium?

Question illustration
A
a feet
B
b feet
C
h feet
D
k feet
11

Which measure is of an angle that is coterminal with a 95° angle?

A
95° – (1,450n)°, for any integer n
B
95° – (1,080n)°, for any integer n
C
95° – (780n)°, for any integer n
D
95° – (340n)°, for any integer n
12

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is , what are the values of a and k?

Question illustration
A
a = –60; k = 20
B
a = –50; k = 30
C
a = –30; k = 50
D
a = –20; k = 60
13

What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

Question illustration
A
5.8 ft
B
6.3 ft
C
27.5 ft
D
69.1 ft
14

The graph of which function passes through (0,3) and has an amplitude of 3?

A
f (x) = sine (x) + 3
Option A
B
f (x) = cosine (x) + 3
Option B
C
f (x) = 3 sine (x)
Option C
D
f (x) = 3 cosine (x)
Option D
15

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is , what are the values of a and k?

Question illustration
A
a = –60; k = 20
B
a = –50; k = 30
C
a = –30; k = 50
D
a = –20; k = 60

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