To find the range of the function [tex]\( y = 2x - 5 \)[/tex] for the given domain [tex]\( D = \{-2, 0, 2, 4\} \)[/tex], we need to substitute each value of the domain into the function and calculate the corresponding [tex]\( y \)[/tex] values.
Let's go through each value in the domain step-by-step:
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 2(-2) - 5 = -4 - 5 = -9
\][/tex]
So, when [tex]\( x = -2 \)[/tex], [tex]\( y = -9 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 2(0) - 5 = 0 - 5 = -5
\][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = -5 \)[/tex].
3. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2(2) - 5 = 4 - 5 = -1
\][/tex]
So, when [tex]\( x = 2 \)[/tex], [tex]\( y = -1 \)[/tex].
4. For [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 2(4) - 5 = 8 - 5 = 3
\][/tex]
So, when [tex]\( x = 4 \)[/tex], [tex]\( y = 3 \)[/tex].
Now, we collect all the [tex]\( y \)[/tex] values obtained:
[tex]\[
R = \{-9, -5, -1, 3\}
\][/tex]
Therefore, the range of the function for the given domain is [tex]\(\{-9, -5, -1, 3\}\)[/tex].
The correct answer is:
[tex]\[ R: \{-9, -5, -1, 3\} \][/tex]
