Question

what are the domain and range of this relation?

domain: {-1, 1, 4}
range: {-5, 2, 3, 4}

domain: {-1, 1, 4}
range: {-5, 2, 3, 5}

domain: {-1, 0, 4}
range: {-5, 2, 3, 4}

domain: {-1, 0, 4}
range: {-5, 2, 3, 5}

Explanation:

Step1: Identify the points

From the graph, the points are \((-1, 2)\), \((0, 5)\), \((0, -5)\), \((4, 3)\). Wait, no, looking at the grid: the points are at \(x = -1, y = 2\); \(x = 0, y = 5\); \(x = 0, y = -5\); \(x = 4, y = 3\). Wait, maybe I misread. Wait, the dots: one at \((-1, 2)\), one at \((0, 5)\), one at \((0, -5)\), one at \((4, 3)\)? Wait no, the y-axis: the top dot is at (0,5)? Wait the graph: the y-axis has a dot at (0,5) (since it's on y-axis, x=0), a dot at (-1, 2), a dot at (0, -5), and a dot at (4, 3). Wait, no, let's check x-coordinates (domain) and y-coordinates (range).

Domain is the set of x-values: from the points, x-values are -1, 0, 4 (since ( -1,2), (0,5), (0,-5), (4,3)). So domain is \(\{-1, 0, 4\}\).

Range is the set of y-values: y-values are -5, 2, 3, 5 (from ( -1,2) → y=2; (0,5) → y=5; (0,-5) → y=-5; (4,3) → y=3). So range is \(\{-5, 2, 3, 5\}\).

Now check the options: the last option (fourth) has domain \(\{-1, 0, 4\}\) and range \(\{-5, 2, 3, 5\}\).

Wait, let's re-express:

Points:

1. (-1, 2) → x=-1, y=2

1. (0, 5) → x=0, y=5

1. (0, -5) → x=0, y=-5

1. (4, 3) → x=4, y=3

So domain (x-values): -1, 0, 4 → \(\{-1, 0, 4\}\)

Range (y-values): -5, 2, 3, 5 → \(\{-5, 2, 3, 5\}\)

So the correct option is the fourth one: domain: \(\{-1, 0, 4\}\), range: \(\{-5, 2, 3, 5\}\)

Step2: Match with options

Looking at the options, the fourth option (bottom right) has domain \(\{-1, 0, 4\}\) and range \(\{-5, 2, 3, 5\}\), which matches our calculation.

Answer:

domain: \(\{-1, 0, 4\}\), range: \(\{-5, 2, 3, 5\}\) (the fourth option: domain: \(\{-1, 0, 4\}\), range: \(\{-5, 2, 3, 5\}\))