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Identity Function: Domain, Range, and Graph

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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</li> </ul> Signup and view all the answers

If x = π/18, what is the value of the expression (cos 9x - cos 5x)/(sin 17x - sin 3x)?

Undefined Signup and view all the answers

What is the relationship between the expressions (cos 9x - cos 5x) and - (sin 2x)?

They are equal only for specific x values. Signup and view all the answers

What is the simplified form of (cos 9x - cos 5x)/(sin 17x - sin 3x)?

<ul> <li>(sin 2x)/(cos 10x)</li> </ul> Signup and view all the answers

In the expression (cos 9x - cos 5x)/(sin 17x - sin 3x), what will be the value if x = 0?

Undefined Signup and view all the answers

Which of the following is NOT equivalent to - (sin 2x)/(cos 10x)?

(cos 7x - cos x)/(sin 15x - sin x) Signup and view all the answers

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 = π/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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Description

This quiz covers the definition of an identity function, including its domain and range. It also explores how the domain and range are represented in the graph of an identity function. Test your knowledge on the characteristics of an identity function.