To determine which statements are true, let’s evaluate the function [tex]\( f(x) = 8(2-x) + 12 \)[/tex] at the given points [tex]\( x = 3 \)[/tex] and [tex]\( x = 9 \)[/tex].
1. Evaluating [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = 8(2-3) + 12
\][/tex]
Start by calculating inside the parentheses:
[tex]\[
2 - 3 = -1
\][/tex]
Next, multiply by 8:
[tex]\[
8 \cdot (-1) = -8
\][/tex]
Finally, add 12:
[tex]\[
-8 + 12 = 4
\][/tex]
So, [tex]\( f(3) = 4 \)[/tex].
2. Evaluating [tex]\( f(9) \)[/tex]:
[tex]\[
f(9) = 8(2-9) + 12
\][/tex]
Start by calculating inside the parentheses:
[tex]\[
2 - 9 = -7
\][/tex]
Next, multiply by 8:
[tex]\[
8 \cdot (-7) = -56
\][/tex]
Finally, add 12:
[tex]\[
-56 + 12 = -44
\][/tex]
So, [tex]\( f(9) = -44 \)[/tex].
Now, let's check the statements:
1. [tex]\( f(3) = 1 \)[/tex] is false since [tex]\( f(3) = 4 \)[/tex].
2. [tex]\( f(9) = 13 \)[/tex] is false since [tex]\( f(9) = -44 \)[/tex].
Therefore, none of the given statements are true based on our evaluations of the function at [tex]\( x = 3 \)[/tex] and [tex]\( x = 9 \)[/tex].
