Question
Identify the amplitude and period of
. Then identify the graph of the function and describe the graph of
as a transformation of the graph of its parent functi)
The amplitude is
and the period is
.
The amplitude is
Ask by Bates Rowe. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Biên độ của hàm
là
, và chu kỳ là
. Đồ thị của hàm
có biên độ lớn hơn và chu kỳ ngắn hơn so với đồ thị hàm sin cơ bản, dao động giữa
và
trong khoảng từ
đến
.
Solution

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Mind Expander
The period of the function
can be determined using the formula
, where
is the coefficient of
. Here,
, so the period is
.
When it comes to the graph,
is a vertical stretch of the parent function
by a factor of 3, making it reach a maximum of 3 and a minimum of -3. Additionally, the graph compresses horizontally due to the factor of 2, resulting in cycles that complete faster—in this case, they repeat every
units instead of
. Thus, you see steeper waves that oscillate between 3 and -3!