In math practice test on function or mapping students can practice the different types of questions related to functions.
1. Which of the following relations are functions?
Give reasons.
(a) R₁ = {(1, 7) (2, 7) (4, 7) (6, 7)}
(b) R₂ = {(1, 2) (1, 3) (1, 4) (1, 5)}
(c) R₃ = {(x, y) (y, z) (z, t) (t, v)}
2. Which of the following arrow diagram represents functions?
3. Let A = {3, 5, 7} and B {1, 2, 3, 4}.
Find if R = {(3, 2) (5, 4) (7, 4)1 is a mapping from A to B.
4. If A = {a, b, c, d} B = {e, f, g}
Is R = {(a, e) (a, f) (a, g) (b, e) (b, f) (b, g) (c, e) (c, f) (d, g)} a function from A to B.
Give reasons to support your answer.
5. If x, y∈{0, 1, 2, 3, 4, 5}
Then, which of the following are function in the given set?
(a) f₁ = {(x, y) : y = x  1}
(b) f₂ = {(x, y) : x + y < 3}
(c) f₃ = {(x, y) : x > y}
(d) f₄ = {(x, y) : x + y = 4}
6. Let A = {3, 2, 1, 0, 1, 2, 3} and B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
Consider the rule f(x) = x².
Find domains (f) and range (f).
7. Given f(x) = 3x – 1. Find:
(i) f(2) (ii) f(5) (iii) f(0)
8. Let f(x) = x² + 1, x∈R, find,
(a) f(2)  f(1)
(b) f(1)  f(0)
(c) f(2)  f(3)
9. Let f(x) = ((4x – 3))/((5x + 1)) , x ∈ R. Find:
(a) f(1) (b) f(1) (c) f(1) + f(1)
10. If f(x) = 5x + 3, x∈R.
If f(x) = 13, find the value of x.
11. A function f : R → R is defined by f(x) = x³.
Determine range of f.
12. What is difference between relation and a function? Is every relation a function? Why?
13. Let A = {1, 0, 1, 2} and B = {0, 1, 2, 3, 4, 5}.
Consider a rule f(x) = x².
Find the domain (f) and range (f).
14. Let A = {1, 1, 2, 2, 3, 3} and B = {1, 4, 9}.
Consider the rule f(x) = x², where x∈A.
Draw the arrow diagram to represent the rule f(x) = x² from A to B. Also, find domain and range of mapping.
Answers for practice test on function or mapping are given below to check the exact answers of the questions.
1. (c), every element in the domain has unique image in the range.
2. (b), (e), (f)
3. Yes
4. No, first component is repeated
5. None
6. Domain = {3, 2, 1, 0, 1, 2, 3} Range = {0, 1, 4, 9}
7. (i) 7
(ii) 14
(iii) 1
8. (a) 3
(b) 1
(c) 5
9. (a) 7/4
(b) 1/6
(c) 22/12
10. 2
11. (a) {8}
(b) {1}
13. Domain = (1, 0, 1, 21} Range = {1, 0, 4}
14.
Domain = {1, 1, 2, 2, 3, 3} Range = {1, 4, 9}
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