Question

what are the domain and range of this function? graph of a coordinate plane with points at (-5,4), (5,4), (3,-1), (4,-4)
options:

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

Explanation:

Step1: Identify the x - coordinates (domain)

The points on the graph have x - coordinates (from left to right): - 5, 3, 4, 5. So the domain is the set of these x - values, which is $\{-5,3,4,5\}$.

Step2: Identify the y - coordinates (range)

The y - coordinates of the points are 4, - 1, - 4, 4. After removing duplicates, the range is the set of these y - values, which is $\{-4, - 1,4\}$.

Looking at the options, the one with domain $\{-5,3,4,5\}$ and range $\{-4, - 1,4\}$ is the correct one.

Answer:

domain: $\{-5, 3, 4, 5\}$, range: $\{-4, -1, 4\}$ (the option with domain $\{-5, 3, 4, 5\}$ and range $\{-4, -1, 4\}$)