Question

1. x = {(-1, 0), (0, 5), (4, 5), (6, 8)}

draw a mapping diagram illustrating each relation.

1. g = {(-6, 5), (-2, 5), (1, -3), (5, 6)}
2. i = {(0, 5), (1, -7), (3, -7), (5, 0)}
3. m = {(2, 6), (3, 6), (18, 6), (20, 6)}
4. e = {(-2, -1), (-2, 2), (3, 1), (3, 4)}
5. y = {(-2, 3), (2, 4), (3, 6), (7, -2)}
6. h = {(4, 7), (-6, 2), (0, -3), (-6, 6)}
7. k = {(3, 5), (-2, 5), (8, 17), (9, 5)}
8. n = {(1, -9), (1, -6), (1, 5), (-1, 8)}

b. exercises
list the set of ordered pairs for each relation.

1. ( y = x + 2 ); ( d = {-3, -2, 1} )
2. ( y = x - 5 ); ( d = {-2, 4, 6, 8} )
3. ( y = 3x ); ( d = {-3, 0, 3, 6} )
4. ( y = 0.5x ); ( d = {4, 6, 8, 10} )
5. ( y = \frac{2}{3}x ); ( d = {-6, 0, 3, 9} )
6. ( y = 2x - 3 ); ( d = {-4, -2, 3, 6} )

list the ordered pairs for each relation and then graph the relation.

1. ( y = 2x ); ( d = {-2, 0, 2} )
2. ( y = x - 2 ); ( d = {-1, 3, 5} )
3. ( y = -x + 3 ); ( d = {-2, 1, 3} )
4. ( y = -\frac{3}{2}x ); ( d = {-2, 0, 2} )
5. ( y = 2x + 1 ); ( d = {-3, -1, 1} )
6. ( y = x - 0.5 ); ( d = {-4, 0, 4} )

state the domain and range of each relation.
33.
34.
35.
(3, 2)
(-4, 2)
(2, 1)

Explanation:

Let's solve problem 23: \( y = 3x \); \( D = \{-3, 0, 3, 6\} \)

Step 1: Substitute \( x = -3 \) into \( y = 3x \)

To find the corresponding \( y \)-value when \( x = -3 \), we use the equation \( y = 3x \). Substituting \( x = -3 \) gives:
\( y = 3(-3) = -9 \)
So the ordered pair is \( (-3, -9) \).

Step 2: Substitute \( x = 0 \) into \( y = 3x \)

Substituting \( x = 0 \) into the equation:
\( y = 3(0) = 0 \)
The ordered pair is \( (0, 0) \).

Step 3: Substitute \( x = 3 \) into \( y = 3x \)

For \( x = 3 \):
\( y = 3(3) = 9 \)
The ordered pair is \( (3, 9) \).

Step 4: Substitute \( x = 6 \) into \( y = 3x \)

Substituting \( x = 6 \):
\( y = 3(6) = 18 \)
The ordered pair is \( (6, 18) \).

Answer:

The set of ordered pairs for the relation \( y = 3x \) with domain \( D = \{-3, 0, 3, 6\} \) is \( \{(-3, -9), (0, 0), (3, 9), (6, 18)\} \).