Math Problem Statement
Solution
The graph in the image shows a function that is periodic and includes a discontinuity at . Based on its shape, we can identify the function as:
Key features of the graph:
- The function is undefined at , corresponding to the vertical asymptotes.
- The graph exhibits periodicity with a period of .
- At , the function value is 0.
- The behavior of the function aligns with the tangent's steep increase and vertical asymptotes.
Would you like further details about the function or its properties? Here are some related questions:
- What is the domain and range of the tangent function?
- How can the tangent function be derived from sine and cosine?
- What are the asymptotes of the tangent function, and how are they calculated?
- How does the period of compare with other trigonometric functions?
- How would the graph of change if a transformation (e.g., vertical stretch or shift) is applied?
Tip: Remember that the tangent function is not defined at points where , as .
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Math Problem Analysis
Mathematical Concepts
Trigonometric Functions
Graph Analysis
Periodicity
Formulas
f(x) = tan(x)
tan(x) = sin(x) / cos(x)
Theorems
Periodicity of Trigonometric Functions
Asymptotes of Tangent Function
Suitable Grade Level
Grades 10-12
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