Sure, let's solve this step-by-step:
1. Start with the given equation:
[tex]\[
6c = 2p - 10
\][/tex]
2. We need to express [tex]\( p \)[/tex] in terms of [tex]\( c \)[/tex]. Begin by isolating [tex]\( p \)[/tex]:
[tex]\[
2p = 6c + 10
\][/tex]
3. Now, solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{6c + 10}{2}
\][/tex]
4. Simplify the expression on the right-hand side:
[tex]\[
p = 3c + 5
\][/tex]
5. Now we can write this in function notation, where [tex]\( c \)[/tex] is the independent variable and [tex]\( p \)[/tex] is the dependent variable. Denoting the function as [tex]\( f(c) \)[/tex], we have:
[tex]\[
f(c) = 3c + 5
\][/tex]
So, the equation in function notation, where [tex]\( c \)[/tex] is the independent variable, is:
[tex]\[
f(c) = 3c + 5
\][/tex]
From the given choices, the correct answer is:
[tex]\[
f(c) = 3c + 5
\][/tex]
