Math Problem Statement

answer this correctly

Given the following sinusoidal graph, determine the domain.

Solution

The question asks for the domain of the given sinusoidal graph. The domain of a sinusoidal function is the set of all possible input values (x-values) for which the function is defined. A standard sinusoidal graph, like the one shown, typically has a domain of all real numbers.

Since the graph is continuous without breaks or restrictions on the x-axis, we conclude that the domain is (,)(-\infty, \infty), which corresponds to option d.

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Here are some related questions you might find interesting:

  1. How can you find the amplitude of a sinusoidal graph?
  2. What is the period of the sinusoidal graph in the image?
  3. How do you determine the range of a sinusoidal function from its graph?
  4. What transformations affect the domain and range of a sinusoidal function?
  5. How does the phase shift of a sinusoidal graph impact its domain?

Tip: Sinusoidal functions, such as sine and cosine, have domains that are always (,)(-\infty, \infty), as they are periodic and do not have any undefined points.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sinusoidal Functions
Domain and Range

Formulas

Domain of sine and cosine functions: (-∞, ∞)

Theorems

The domain of sine and cosine functions is all real numbers.

Suitable Grade Level

Grades 9-12