Let's start by understanding the problem's requirements. We are given a domain of values: [tex]\(\{-2, 1, 5\}\)[/tex]. We need to find the range by applying the relation [tex]\(y = 4x\)[/tex] to each element of the domain.
Step-by-Step Solution:
1. Substitute each element of the domain into the relation [tex]\( y = 4x \)[/tex]:
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 4 \cdot (-2) = -8
\][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 4 \cdot 1 = 4
\][/tex]
- For [tex]\( x = 5 \)[/tex]:
[tex]\[
y = 4 \cdot 5 = 20
\][/tex]
2. Collect the results to form the range:
The values we have calculated are [tex]\(-8\)[/tex], [tex]\(4\)[/tex], and [tex]\(20\)[/tex]. Therefore, the range for this relation is:
[tex]\[
\{-8, 4, 20\}
\][/tex]
3. Compare the calculated range with the given options:
- Option 1: [tex]\(\{11, -1, -17\}\)[/tex]
- Option 2: [tex]\(\{-1, 4, 8\}\)[/tex]
- Option 3: [tex]\(\{-11, 1, 17\}\)[/tex]
- Option 4: [tex]\(\{-5, 7, 23\}\)[/tex]
Comparing our calculated range [tex]\(\{-8, 4, 20\}\)[/tex] with the options, none of the given options match exactly with our calculated range. If the problem involves a different target range or correct selections by choices, typically the choices provided might need scrutiny strictly.
Therefore, based on the step-by-step calculations, it seems none of the provided options directly match the calculated range. Possibly, the correct input option to match this calculation scenario would be logically re-examined or one should verify computation or formulated exact constraints in choice form.
However, ideally the expected correct choices might likely be factually based, then the system context of deriving [tex]\(\{-8, 4, 20\}\)[/tex] suggests verifying input provided clues variability analyzed correctly in scenarios overall.
