AnswersS1S-OC Pre-Calculus A E3700 - AGGraphing Sine and Cosine Functions

Graphing Sine and Cosine Functions Answers

0 verified answers2 views
1
Free Preview

What is the equation of a sine function with an amplitude of 2 and a period of 4π?

A
y = one-half sine (2 x)
Option A
B
y = one-half sine (4 pi x)
Option B
C
y = 2 sine (one-half x)
Option C
D
y = 2 sine (4 pi x)
Option D
2
Free Preview

The musical note E can be modeled by the function, y = asin(1320πx), where a = 1 and x is the time in seconds. Playing note E on your computer, you notice that it is not loud enough to be heard across the room.What change can you make to the function to make note E louder than the original?

A
Let a < 0.
B
Let a > 0.
C
Let a > 0 and a < 1.
D
Let a > 1 or a < –1.
3

If the function y = sinx is transformed to , how do the amplitude and period change?

Question illustration
A
The amplitude increases, and the period decreases.
B
The amplitude increases, and the period increases.
C
The amplitude decreases, and the period decreases.
D
The amplitude decreases, and the period increases.
4

What is the y-intercept of the function ?

Question illustration
A
(negative one-half, 0)
Option A
B
(0, negative one-half)
Option B
C
(0, three-halves)
Option C
D
(Three-halves, 0)
Option D
5

Which statement illustrates why cosine is an even function?

A
Cosine (StartFraction pi Over 4 EndFraction) = negative cosine (StartFraction 5 pi Over 4 EndFraction)
Option A
B
Cosine (StartFraction pi Over 4 EndFraction) = negative cosine (StartFraction 4 pi Over 4 EndFraction)
Option B
C
Cosine (negative StartFraction pi Over 4 EndFraction) = cosine (StartFraction 4 pi Over 4 EndFraction)
Option C
D
Cosine (StartFraction negative 7 pi Over 6 EndFraction) = cosine (StartFraction 5 pi Over 4 EndFraction)
Option D
6

Consider the function y = acos(bx), where a > 0 and b > 0. Which change affects the locations of the x-intercepts of the graph?

A
Decrease a.
B
Decrease b.
C
Change the sign of a.
D
Change the sign of b.
7

What is one characteristic of the cosine function?

A
It is an odd function.
B
It has a period equal to π.
C
Its graph is symmetric about the y-axis.
D
Its domain is between –1 and 1 and is inclusive.
8

Consider the function y = asin(bx), where a > 0 and b > 0. Which change compresses the graph vertically?

A
Increase a.
B
Decrease a.
C
Increase b.
D
Decrease b.
9

Which graph represents the function y = –2cos(2πx)?

A
On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at StartFraction 2.5 pi Over 4 EndFraction. It crosses the y-axis at (0, negative 2).
Option A
B
On a coordinate plane, a function has a maximum of 2 and minimum of 2. It completes one period at one-fourth pi. It crosses the y-axis at (0, negative 2).
Option B
C
On a coordinate plane, a function has a maximum of 2 and minimum of 2. It completes one period between StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 4 EndFraction. It decreases through the y-axis at (0, 0).
Option C
D
On a coordinate plane, a function has a maximum of 2 and minimum of 2. It completes one period between StartFraction pi Over 4 EndFraction and StartFraction pi Over 2 EndFraction. It decreases through the y-axis at (0, 0).
Option D
10

On the interval 0 ≤ x ≤ 2π, what are the x-intercepts of y = sinx?

A
0, StartFraction pi Over 2 EndFraction, and StartFraction 3 pi Over 2 EndFraction
Option A
B
0, π, and 2π
C
StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction
Option C
D
π and 2π only

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Graphing Sine and Cosine Functions

Quiz
10 verified answers

Inverse Trigonometric Functions

Quiz
10 verified answers

Inverse Trigonometric Functions

Graphing Sine and Cosine Functions Answers —…