To write the function represented by the equation [tex]\( 9x + 3y = 12 \)[/tex] in function notation with [tex]\( x \)[/tex] as the independent variable, we need to isolate [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
1. Start with the original equation:
[tex]\[
9x + 3y = 12
\][/tex]
2. Subtract [tex]\( 9x \)[/tex] from both sides to isolate the [tex]\( 3y \)[/tex] term:
[tex]\[
3y = 12 - 9x
\][/tex]
3. Divide both sides by [tex]\( 3 \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{12 - 9x}{3}
\][/tex]
4. Simplify the right-hand side:
[tex]\[
y = \frac{12}{3} - \frac{9x}{3}
\][/tex]
[tex]\[
y = 4 - 3x
\][/tex]
Now that we have [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we can rewrite the equation as a function [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = -3x + 4
\][/tex]
Therefore, the function in notation form is:
[tex]\[
f(x) = -3x + 4
\][/tex]
Among the given choices, the correct function notation is:
[tex]\[
f(x) = -3x + 4
\][/tex]
