Answer :
To identify which equation correctly represents the given equation [tex]\( y - 6x - 9 = 0 \)[/tex] in function notation with [tex]\( x \)[/tex] as the independent variable, let's go through the steps to rewrite the equation.
1. Start with the original equation:
[tex]\[ y - 6x - 9 = 0 \][/tex]
2. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 6x + 9 \][/tex]
3. In function notation, we express [tex]\( y \)[/tex] as [tex]\( f(x) \)[/tex] because [tex]\( y \)[/tex] is dependent on the independent variable [tex]\( x \)[/tex]:
[tex]\[ f(x) = 6x + 9 \][/tex]
Given the options:
- [tex]\( f(x) = 6x + 9 \)[/tex]
- [tex]\( f(x) = \frac{1}{6}x + \frac{3}{2} \)[/tex]
- [tex]\( f(y) = 6y + 9 \)[/tex]
- [tex]\( f(y) = \frac{1}{6}y + \frac{3}{2} \)[/tex]
The correct equation written in function notation with [tex]\( x \)[/tex] as the independent variable is:
[tex]\[ f(x) = 6x + 9 \][/tex]
So, the first option [tex]\( f(x) = 6x + 9 \)[/tex] is correct. Therefore, the answer to the question is:
[tex]\[ 1 \][/tex]
1. Start with the original equation:
[tex]\[ y - 6x - 9 = 0 \][/tex]
2. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = 6x + 9 \][/tex]
3. In function notation, we express [tex]\( y \)[/tex] as [tex]\( f(x) \)[/tex] because [tex]\( y \)[/tex] is dependent on the independent variable [tex]\( x \)[/tex]:
[tex]\[ f(x) = 6x + 9 \][/tex]
Given the options:
- [tex]\( f(x) = 6x + 9 \)[/tex]
- [tex]\( f(x) = \frac{1}{6}x + \frac{3}{2} \)[/tex]
- [tex]\( f(y) = 6y + 9 \)[/tex]
- [tex]\( f(y) = \frac{1}{6}y + \frac{3}{2} \)[/tex]
The correct equation written in function notation with [tex]\( x \)[/tex] as the independent variable is:
[tex]\[ f(x) = 6x + 9 \][/tex]
So, the first option [tex]\( f(x) = 6x + 9 \)[/tex] is correct. Therefore, the answer to the question is:
[tex]\[ 1 \][/tex]
