To determine the range of the function [tex]\( f(x) = 4x + 9 \)[/tex] given the domain [tex]\( D = \{-4, -2, 0, 2\} \)[/tex], we need to evaluate the function at each value in the domain.
1. Calculate [tex]\( f(-4) \)[/tex]:
[tex]\[
f(-4) = 4(-4) + 9 = -16 + 9 = -7
\][/tex]
2. Calculate [tex]\( f(-2) \)[/tex]:
[tex]\[
f(-2) = 4(-2) + 9 = -8 + 9 = 1
\][/tex]
3. Calculate [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 4(0) + 9 = 0 + 9 = 9
\][/tex]
4. Calculate [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 4(2) + 9 = 8 + 9 = 17
\][/tex]
So, the values of the function for the given domain are:
[tex]\[
\{-7, 1, 9, 17\}
\][/tex]
Therefore, the range [tex]\( R \)[/tex] of the function [tex]\( f(x) = 4x + 9 \)[/tex] for the domain [tex]\( D = \{-4, -2, 0, 2\} \)[/tex] is:
[tex]\[
R = \{-7, 1, 9, 17\}
\][/tex]
The correct answer is:
C. [tex]\( R = \{-7, 1, 9, 17\} \)[/tex]
