Sure! Let's convert the given equation [tex]\( 6c = 2p - 10 \)[/tex] into function notation. Here we are to express it with [tex]\( c \)[/tex] as the independent variable and rewrite the equation to represent a function of [tex]\( p \)[/tex].
1. Start with the given equation:
[tex]\[
6c = 2p - 10
\][/tex]
2. To isolate [tex]\( p \)[/tex], we divide both sides of the equation by 2:
[tex]\[
3c = p - 5
\][/tex]
3. Next, we solve for [tex]\( p \)[/tex] by adding 5 to both sides of the equation:
[tex]\[
3c + 5 = p
\][/tex]
4. Rewrite in function notation, where [tex]\( f(p) \)[/tex] represents [tex]\( p \)[/tex] in terms of [tex]\( c \)[/tex]:
[tex]\[
f(p) = 3c + 5
\][/tex]
Therefore, the function notation for the given equation [tex]\( 6c = 2p - 10 \)[/tex], where [tex]\( c \)[/tex] is the independent variable, is:
[tex]\[
f(p) = 3c + 5
\][/tex]
