What to create	Exam
Which subject	Mathematics
What age group	Year or Grade 10
What topic	Domaine and Range continuous and discontinuous functions and 1-to-1
Question types	Close-ended
Number of questions	10
Number of answers	4
Correct answers	Exactly 1
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Grade 10 Mathematics Quiz: Domain and Range of Functions

Instructions:

Answer the following questions related to the domain, range, continuous and discontinuous functions, and one-to-one functions. Choose the correct answer from the options provided.

Questions:

1. What is the domain of the function ( f(x) = \sqrt{x - 3} )?

   • A. ( x \geq 3 )
   • B. ( x > 3 )
   • C. All real numbers
   • D. ( x \leq 3 )

2. For the function ( g(x) = \frac{1}{x - 2} ), which of the following is the range?

   • A. All real numbers except 0
   • B. All real numbers
   • C. ( y \geq 0 )
   • D. ( y > 0 )

3. Which of the following functions is discontinuous?

   • A. ( h(x) = 2x + 3 )
   • B. ( k(x) = \frac{x^2 - 9}{x - 3} )
   • C. ( m(x) = |x| )
   • D. ( n(x) = x^2 )

4. What is the domain of the function ( p(x) = \frac{1}{x^2 - 1} )?

   • A. All real numbers except ( x = 1 ) and ( x = -1 )
   • B. All real numbers
   • C. ( x \neq 0 )
   • D. ( x \geq 1 )

5. For the function ( q(x) = 3x - 4 ) to be one-to-one, what must be true?

   • A. It must have a horizontal line test
   • B. It must equal zero at some point
   • C. It cannot have any zeros
   • D. Its domain must be restricted

6. Which type of function is represented by ( r(x) = x^3 - 3x + 1 )?

   • A. Discontinuous function
   • B. Continuous function
   • C. Constant function
   • D. One-to-one function

7. What is the range of the quadratic function ( s(x) = x^2 - 5 )?

   • A. All real numbers less than -5
   • B. All real numbers greater than or equal to -5
   • C. All real numbers
   • D. ( y = -5 )

8. Identify the correct relationship for the function ( t(x) = \frac{x + 5}{x + 2} ) around its vertical asymptote.

   • A. Continuous everywhere
   • B. Discontinuous at ( x = -2 )
   • C. One-to-one
   • D. Has a horizontal asymptote

9. Which of the following graphs represents a one-to-one function?

   • A. The graph of ( y = x^2 )
   • B. The graph of ( y = e^x )
   • C. The graph of ( y = \sin(x) )
   • D. The graph of ( y = |x| )

10. What is the domain of the function ( u(x) = \ln(x - 1) )?

    • A. ( x > 1 )
    • B. All real numbers
    • C. ( x \geq 1 )
    • D. ( x < 1 )

Good luck with your answers!