Math Problem Statement
Determine the correct equation of the following graph.
Solution
The graph shows a periodic function, and it appears to be a sine or cosine function. To determine the correct equation, we need to analyze the graph's characteristics: amplitude, period, phase shift, and vertical shift.
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Amplitude: The maximum value is approximately 4, and the minimum value is approximately -4. Therefore, the amplitude is 4.
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Period: The distance between two consecutive peaks (or troughs) determines the period. From the graph, it appears that the period is 60 units (from -30 to 30 or from 0 to 60).
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Phase Shift: The graph appears to cross the y-axis at the origin (0,0), which suggests there is no horizontal shift for the cosine function.
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Vertical Shift: The graph oscillates around the x-axis (y=0), indicating there is no vertical shift.
Given these characteristics, the equation could be of the form .
Plugging in the values:
- (amplitude)
- (since the period is 60)
- (no phase shift)
- (no vertical shift)
Thus, the equation of the graph is:
Would you like further details or have any questions?
Here are five more questions you might want to ask:
- How do you determine the amplitude of a graph?
- What is the significance of the period in trigonometric functions?
- How do you find the phase shift of a function from its graph?
- What are the steps to convert a trigonometric function into its general form?
- Can you explain how vertical shifts affect the graph of a trigonometric function?
Tip: When identifying the equation of a trigonometric function from its graph, carefully note the amplitude, period, phase shift, and vertical shift, as these parameters define the function's behavior.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Formulas
Trigonometric function: y = A cos(Bx + C) + D
Theorems
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Suitable Grade Level
High School
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