What is the primary focus when translating sine and cosine functions?

Transformations of Sine and Cosine Functions

Interactive Video
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Mathematics
•
9th - 10th Grade
•
Hard

Thomas White
FREE Resource
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8 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Modifying the function's domain
Translating the function horizontally and vertically
Adjusting the function's frequency
Changing the function's amplitude
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a phase shift in the context of periodic functions?
A vertical shift of the function
A change in the function's amplitude
A horizontal shift inside the function
A modification of the function's period
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the equation y = a * sin(bx - h) + k, what does 'a' represent?
The period
The vertical shift
The phase shift
The amplitude
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does a negative sign in front of the amplitude affect the sine function?
It changes the function's period
It reflects the function over the x-axis
It shifts the function vertically
It modifies the function's phase shift
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the effect of a horizontal shift of f(x - h) on the graph of a sine function?
The graph shifts h units to the left
The graph shifts h units to the right
The graph shifts h units upward
The graph shifts h units downward
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the equation y = cos(x - π) + 5, what is the vertical shift?
5 units down
π units to the right
5 units up
π units to the left
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When combining transformations, what is the first step in graphing the function?
Identify the amplitude
Plot the reference graph
Calculate the period
Determine the phase shift
8.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you write an equation for a cosine function that is shifted up by 3 units?
y = cos(x) + 3
y = cos(x) - 3
y = cos(x + 3)
y = cos(x - 3)
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