To find the range of the function [tex]\( f(x) = x^2 - 5x \)[/tex] for the given domain [tex]\(\{2, 4, 7\}\)[/tex], we will evaluate the function at each value in the domain:
1. Evaluating at [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 2^2 - 5 \cdot 2 = 4 - 10 = -6
\][/tex]
2. Evaluating at [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = 4^2 - 5 \cdot 4 = 16 - 20 = -4
\][/tex]
3. Evaluating at [tex]\( x = 7 \)[/tex]:
[tex]\[
f(7) = 7^2 - 5 \cdot 7 = 49 - 35 = 14
\][/tex]
So, the range of the function [tex]\( f(x) = x^2 - 5x \)[/tex] for the domain [tex]\(\{2, 4, 7\}\)[/tex] is:
[tex]\[
\{-6, -4, 14\}
\][/tex]
