Question

for the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
d: {0,1,2,-4}
r: {1,-3,-4,1}
d: {1,-3,-4,}
r: {0,1,2,-4}
d: {-4,0,1,2}
r:{-4,-3,1}
d: {0,1,2,3,4}
r:{1,-3,-4}

Explanation:

Step1: Recall domain/range definitions

Domain: set of all x - values (first elements of ordered pairs).
Range: set of all y - values (second elements of ordered pairs), with duplicates removed.

Given function: \(\{(0,1),(1, - 3),(2,-4),(-4,1)\}\)

Step2: Find domain

Extract x - values: \(0,1,2,-4\). Sort them: \(-4,0,1,2\).

Step3: Find range

Extract y - values: \(1,-3,-4,1\). Remove duplicate \(1\), so range is \(\{-4,-3,1\}\).

Step4: Match with options

Check each option:

• First option: Range has duplicate \(1\) (invalid, range should have unique values).
• Second option: Domain has y - values (invalid, domain is x - values).
• Third option: Domain \(\{-4,0,1,2\}\), Range \(\{-4,-3,1\}\) (matches).
• Fourth option: Domain and range incorrect (values not in ordered pairs).

Answer:

C. D: \(\{-4, 0, 1, 2\}\)
R: \(\{-4, -3, 1\}\)