Identity Function: Domain, Range, and Graph

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Questions and Answers

What is the domain and range of an identity function?

  • Domain: All real numbers; Range: All real numbers (correct)
  • Domain: Natural numbers only; Range: Integers
  • Domain: All integers; Range: All integers
  • Domain: Positive real numbers only; Range: Negative real numbers

In the graph of an identity function, how are the domain and range represented?

  • Both Domain and Range are on the x-axis
  • Domain is the x-axis, Range is the y-axis (correct)
  • Domain is the y-axis, Range is the x-axis
  • Both Domain and Range are on the y-axis

Which of the following statements about an identity function is true?

  • It is a constant function with f(x) = x (correct)
  • It is a decreasing function
  • It maps all values to 0
  • It has different values for x and y

What does the given expression simplify to?

<ul> <li>tan 4x (B)</li> </ul>
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If x = π/18, what is the value of the expression (cos 9x - cos 5x)/(sin 17x - sin 3x)?

<p>Undefined (D)</p>
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What is the relationship between the expressions (cos 9x - cos 5x) and - (sin 2x)?

<p>They are equal only for specific x values. (C)</p>
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What is the simplified form of (cos 9x - cos 5x)/(sin 17x - sin 3x)?

<ul> <li>(sin 2x)/(cos 10x) (C)</li> </ul>
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In the expression (cos 9x - cos 5x)/(sin 17x - sin 3x), what will be the value if x = 0?

<p>Undefined (A)</p>
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Which of the following is NOT equivalent to - (sin 2x)/(cos 10x)?

<p>(cos 7x - cos x)/(sin 15x - sin x) (D)</p>
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Study Notes

Identity Function

  • The domain of an identity function is all real numbers, and the range is also all real numbers.
  • In the graph of an identity function, the domain and range are represented by a straight line passing through the origin with a slope of 1.

Trigonometric Expressions

  • If x = Ï€/18, the value of the expression (cos 9x - cos 5x)/(sin 17x - sin 3x) can be evaluated.
  • The expressions (cos 9x - cos 5x) and - (sin 2x) have a relationship, where the former can be simplified to the latter.
  • The simplified form of (cos 9x - cos 5x)/(sin 17x - sin 3x) is - (sin 2x)/(cos 10x).
  • If x = 0, the value of the expression (cos 9x - cos 5x)/(sin 17x - sin 3x) can be evaluated.

Equivalent Expressions

    • (sin 2x)/(cos 10x) has equivalent expressions, but not (sin 10x)/(cos 2x).

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