## Relations and Functions Exercise

1. C = {(2, 5),(4, 9), (6, 13)} is a function.

(a) List the domain of C.

(b) List the range of C.

2. Complete the ordered pairs for the given relations:

(a) y = x − 3 {(0, ), (1, ), (-1, ),(-2, ), ( , 0), (n, ), ( , m)}

(b) y − 2x = 6 {(0, ), (1, ), (-1, ),(-2, ), ( , 0), (n, ), ( , m)}

(c) y = x 2 + 3 {(0, ), (1, ), (-1, ),(-2, ), (n, ), ( , m)}

3. Which of the following relations are also functions?

 (a) (b) (c) (d)

4. D = {(-2, 4), (-1, 1), (0, 0),(1, 1), (2, 4)}

(a) Show this relation:

(i) As an arrow graph.

(ii) As an (x, y) graph.

(b) What is the equation for this relation?

5. For the relation shown:

 (a) List the domain. (b) List the range. (c) Is the relation shown also a function? (d) Write the relation as a set of ordered pairs.

6. Give the equation of the following relations:

(a) {(2, 4), (3, 9), (4, 16)}

(b) {(1, 0), (2, 1), (3, 2)}

(c) {(0, 1), (1, 3), (2, 5)}

7. (a) Rectangles each of width 1 unit are outlined with matchsticks as shown below.

Complete the pattern of numbers in the top part of the table and use the pattern to fill in the lower part.

 Number of matchsticks along each long side Total number of matchsticks 1 4 2 6 3 4 5 42 n 42 m

(b) The line drawn below is the graph of the function y = 0.5x − 1

On the same diagram, draw:

 (i) The line with equation y = x (ii) The line that is the graph of y = 2x + 2