Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - characteristics - Domain and Range.
Test Yourself 1.


 

For each of the questions in the following table,
determine both the domain and the range of the function
unless otherwise indicated.


Answer.Domain: (-∞, 3)
Range: (-∞, 0).
Linear 1. 2x + 3y = 6
Answer. Domain (-∞, ∞)
Range (-∞, ∞) 		2. y = 3
Answer. Domain (-∞, ∞)
Range [3, 3]
  3. x = 2
Answer. Domain [2,2])
Range (-∞, ∞)		 4. y = -14x
Answer. Domain (-∞, ∞)
Range (-∞, ∞)
Quadratic 5.
Answer. Domain (-∞, 5]
Range [0, ∞)		 6. y = 5 - x2
Answer. Domain (-∞, ∞)
Range (-∞, 5])
  7. y = x2 - 3
Answer. Domain (-∞, ∞)
Range [-3, ∞)		 8. y = (x - 3)2 + 2
Other basic combinations.

9. State the domain and range of x2 + y2 = 4?

Answer. Domain [-2, 2]
Range [-2, 2]

 10. Draw a neat sketch of

and label it appropriately. Then state the domain and range of this relationship.

Answer. Domain (-∞, 0.2)U(0.2, ∞)
Range (-∞, 0)U(0, ∞)

 

 11. Draw a neat sketch of

and label it appropriately. Then state the domain and range of this relationship.

Answer. Domain [-1, 5]
Range [-6, 0]		 12. Draw a neat sketch of

and label it appropriately. Then state the domain and range of this relationship.

Answer. Domain (-∞, 2)U (2, ∞)
Range (-∞, 0)U(0, ∞).
 

13. Draw a neat sketch of

.

Label it appropriately and then state the domain and range of this relationship.
Answer.Domain is (-∞, ∞)
Range is (3, ∞).

 14. Draw a neat sketch of

and label it appropriately. Then state the domain and range of this relationship.

Answer. Domain [-1, 5]
Range [-6, 0]
Radicals - one term 15. Write down the domain and range of
Answer.Domain: [-3, +3]
Range: (3, ∞). 		16.Write down the largest natural domain for the function

.

Answer.Domain: (-∞, -3] ∪ [3, ∞)
Range: [0, ∞)
  17. Write down the domain and range of .
Answer.Domain: (1, ∞)
Range: (0, ∞).		 18. Write down the domain and range of
  19. Write down the domain and range of
Answer. Domain: [1, ∞)
Range: [3, ∞).		 20. Write down the domain and range of .
Answer.Domain: (-∞, 1.3)
Range: (2, ∞).
Two terms 21. Write down the domain and range of
Answer.Domain: [1, 3]
Range: [√2, 2]		 22. What is the largest possible domain for the function

Answer. Domain (-∞, 0) ∪ (0, ∞)
Range: (∞, 2] ∪ {2, ∞)