교과서 질문
Graph each function over a one-period interval.
y = 2 tan (¼ x)
712
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Ch. 4 - Graphs of the Circular Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
5장, 문제 16
Match each function with its graph in choices A–I. (One choice will not be used.)
y = -1 + cos x
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검증된 단계별 안내1
Identify the base function in the given equation: here, it is the cosine function, \(\cos x\).
Note the transformation applied to the base function: the function is shifted vertically by \(-1\), so the graph of \(y = \cos x\) is moved down by 1 unit.
Recall the key characteristics of \(y = \cos x\): it has a maximum value of 1, a minimum value of -1, and a midline at \(y=0\). After the vertical shift, the new midline will be at \(y = -1\).
Analyze the amplitude and period: the amplitude remains 1 (since there is no coefficient multiplying \(\cos x\)), and the period remains \(2\pi\).
Match the graph that shows a cosine wave with its midline at \(y = -1\), maximum at 0, minimum at \(-2\), and the usual cosine wave shape starting at a maximum point when \(x=0\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Graphing Transformations of Trigonometric Functions
Understanding how vertical shifts, reflections, and stretches affect the graph of trigonometric functions is essential. For example, y = -1 + cos x represents a cosine graph shifted down by 1 unit. Recognizing these transformations helps match the function to its correct graph.
추천 영상:
4:22
Domain and Range of Function Transformations
Properties of the Cosine Function
The cosine function has a period of 2π, an amplitude of 1, and ranges between -1 and 1. Knowing its shape, maxima, minima, and zeros allows you to identify its graph and distinguish it from sine or other trigonometric functions.
추천 영상:
5:53Graph of Sine and Cosine Function
Function and Graph Matching Techniques
Matching functions to graphs involves analyzing key features such as amplitude, period, phase shift, and vertical shift. Comparing these features systematically enables accurate identification of the correct graph among multiple choices.
추천 영상:
5:53Graph of Sine and Cosine Function
관련 실천
교과서 질문
Match each function in Column I with the appropriate description in Column II.
I
y = 3 sin(2x - 4)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
753
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교과서 질문
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 1/3 tan (3x - π/3)
701
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교과서 질문
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = cot (x/2 + 3π/4)
667
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교과서 질문
Graph each function over a one-period interval.
y = cot (3x)
846
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교과서 질문
Graph each function over a one-period interval. See Examples 1–3.
y = 2 tan x
701
views