Math Problem Statement
Find the domain and range
Solution
The graph you uploaded represents a sinusoidal curve, which appears to be a standard sine or cosine function. Let’s analyze the domain and range.
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Domain: The domain of the sine or cosine function is all real numbers, since the function continues infinitely in both the positive and negative directions along the -axis.
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Range: The range of the sine or cosine function is limited between the maximum and minimum values that the curve reaches on the -axis. From the graph, the curve oscillates between and .
So, the domain is all real numbers, and the range is from to .
Would you like more details or have any questions about this?
Here are 5 related questions you might find interesting:
- What is the period of this sinusoidal function?
- How do amplitude and phase shift affect the sine or cosine graph?
- What is the general equation of a sinusoidal function?
- Can this graph represent a real-world phenomenon? If yes, which one?
- How would this graph change if the amplitude were doubled?
Tip: Always check the amplitude, period, and phase shift when analyzing or sketching sinusoidal graphs!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Functions
Formulas
y = sin(x)
y = cos(x)
Theorems
Properties of sine and cosine functions
Suitable Grade Level
Grades 9-12