To start, we are given the equation [tex]\( 6q = 3s - 9 \)[/tex]. Our goal is to express [tex]\( s \)[/tex] in terms of [tex]\( q \)[/tex] and then put this expression into function notation.
1. Begin with the given equation:
[tex]\[
6q = 3s - 9
\][/tex]
2. To isolate [tex]\( s \)[/tex], first add 9 to both sides of the equation:
[tex]\[
6q + 9 = 3s
\][/tex]
3. Now, divide both sides by 3 to solve for [tex]\( s \)[/tex]:
[tex]\[
\frac{6q + 9}{3} = s
\][/tex]
Simplifying the right-hand side:
[tex]\[
s = \frac{6q}{3} + \frac{9}{3}
\][/tex]
[tex]\[
s = 2q + 3
\][/tex]
4. Now, express [tex]\( s \)[/tex] as [tex]\( f(q) \)[/tex] in function notation:
[tex]\[
f(q) = 2q + 3
\][/tex]
From the options provided, the correct one that matches the function [tex]\( s = 2q + 3 \)[/tex] is:
[tex]\[
f(q) = 2q + 3
\][/tex]
Therefore, the correct choice is [tex]\( f(q) = 2q + 3 \)[/tex].
