If you are searching everywhere for assistance regarding the concept functions then take the help of our Math Practice Test on Functions. Solve as many questions as possible from the Functions Practice Test and get various question models. We have provided step by step solution for several examples of Functions so that you can understand them better. Become familiar with the entire concept of Functions by using the Practice Test on Functions.

- Relations and Mapping
- Ordered Pair
- Cartesian Product of Two Sets
- Relation in Math
- Domain and Range of a Relation
- Practice Test on Math Relation
- Functions or Mapping
- Domain Co-domain and Range of Function

1. Consider A = {4, 5, 6} and B = {3, 5, 7, 8}. Find if R = {(4, 3) (5, 7) (6, 8)} is a mapping from A to B and give reasons to support your answer?

**Solution:**

Since R = {(4, 3) (5, 7) (6, 8)}

No two ordered pairs have the same first components, R is Mapping from A to B.

2. Which of the following relations are functions?

(a) R₁ = {(4, 7) (5, 7) (6, 7) (7, 7)}

(b) R₂ = {(1, 3) (1, 4) (1, 5) (1, 6)}

(c) R₃ = {(a,b) (b, c) (c, d) (d, e)}

**Solution:**

R₃ is a function since each element in one set is associated with a unique element in the other set. Thus, it is a function.

3. Given f(x) = 2x+3 find

(i) f(1) (ii) f(-2) (iii) f(3)

**Solution:**

Given f(x) = 2x+3

(i) f(1) = 2*1+3 = 2+3 = 5

(ii) f(-2) = 2*(-2)+3 = -4+3 = -1

(iii) f(3) = 2*3+3 = 6+3 = 9

4. If f(x) = 4x – 3, x∈R and f(x) = 15 find the value of x?

**Solution:**

Given f(x) = 4x – 3

f(x) = 15

Equating both we can get the value of x as such

4x-3 = 15

4x = 15+3

4x = 18

x = 18/4

= 9/2

5. If A = {a, b, c, d} B = {x, y, z} Is R = {(a, x) (a, y) (a, z) (b, x) (b, y) (b, z) (c, x) (c, y) (d, z)} a function from A to B. Give reasons to support your answer?

**Solution:**

No, Relation R is not a function since the first components are repeated.

6. Which set of ordered pairs is not a function?

**(a)** (3, 2) (2, 6) (3, 5) **(b)** (4, 2) (7, 6) (2, 5)

**(c)** (1, 3) (3, 5) (4, 9) **(d)** (1, 2) (5, 2) (6, 5)

**Solution:**

**(a)** (3, 2) (2, 6) (3, 5)

The above option isn’t a function since the set of ordered pairs given has the repeated first component.

7. Recalling function notation we want x to be y and f(x) = 2x+3/2, find f(y)?

**Solution:**

f(x) = 2x+3/2

since we want function notation x to be y replace x with y in the given function

f(y) = (2y+3)/2

8. The Revenue of a Company is given by R(x) = X^{2}+800X and Cost C(x) = 400X+150. Find the Profit gained by the Company R(x)- C(x)?

**Solution:**

R(x) = X^{2}+800X

C(x) = 400X+150

Profit = R(x)- C(x)

= X^{2}+800X – (400X+150)

= X^{2}+800X – 400X – 150

= X^{2}+ 400X – 150

9. The function S(r) =4πr^{2} gives the surface area of a sphere having radius r. What is the surface area of a sphere for radius 2?

**Solution:**

Given S(r) =4πr^{2}

Substitute 2 in place of the radius in the given function to find surface area of sphere with radius 2.

S(2) = 4.π.2^{2}

= 4π.4

= 16π

Surface Area of Sphere for Radius 2 is 16π.

10. Does the following arrow diagram represent a function?

**Solution:**

Every element in the first set is associated with only element in the other set. Thus, the relation F qualifies to be a function.