Question

1. name the domain and range for each relation. plot the points for each on the coordinate plane. which relation falls along a line?

relation a: (-4, -7), (-2, -3), (0, 1), (1, 3), (3, 7)
domain (x) range (y)

relation b: (0, 5), (0, -5), (5, 0), (-5, 0)
domain (x) range (y)

Explanation:

Step1: Analyze Relation A

For a relation, the domain is the set of all x - values, and the range is the set of all y - values.
For Relation A: \((-4, -7), (-2, -3), (0, 1), (1, 3), (3, 7)\)

• Domain (x - values): \(\{-4, -2, 0, 1, 3\}\)
• Range (y - values): \(\{-7, -3, 1, 3, 7\}\)

To check if it lies on a line, we can calculate the slope between consecutive points.
Slope between \((-4, -7)\) and \((-2, -3)\): \(m=\frac{-3 - (-7)}{-2 - (-4)}=\frac{4}{2} = 2\)
Slope between \((-2, -3)\) and \((0, 1)\): \(m=\frac{1-(-3)}{0 - (-2)}=\frac{4}{2}=2\)
Slope between \((0, 1)\) and \((1, 3)\): \(m=\frac{3 - 1}{1 - 0}=\frac{2}{1}=2\)
Slope between \((1, 3)\) and \((3, 7)\): \(m=\frac{7 - 3}{3 - 1}=\frac{4}{2}=2\)
Since the slope between consecutive points is constant (\(m = 2\)), the points of Relation A lie on a straight line.

Step2: Analyze Relation B

For Relation B: \((0, 5), (0, -5), (5, 0), (-5, 0)\)

• Domain (x - values): \(\{-5, 0, 5\}\)
• Range (y - values): \(\{-5, 0, 5\}\)

The points \((0, 5)\) and \((0, -5)\) lie on the y - axis (a vertical line \(x = 0\)), and the points \((5, 0)\) and \((-5, 0)\) lie on the x - axis (a horizontal line \(y = 0\)). The four points form a cross (intersection of x - axis and y - axis with some points), not a single straight line.

Answer:

Relation A:

• Domain: \(\{-4, -2, 0, 1, 3\}\)
• Range: \(\{-7, -3, 1, 3, 7\}\)
• Lies on a line (since the slope between consecutive points is constant, \(m = 2\))

Relation B:

• Domain: \(\{-5, 0, 5\}\)
• Range: \(\{-5, 0, 5\}\)
• Does not lie on a single line (forms a cross - like shape with points on x - axis and y - axis)

The relation that falls along a line is Relation A.