Answer :
To convert a given equation into function notation with \( x \) as the independent variable, follow these steps:
1. Given equation: \( y - 6x - 9 = 0 \).
2. Isolate \( y \) in terms of \( x \):
[tex]\[ y = 6x + 9 \][/tex]
3. Rewrite this equation in function notation:
The variable \( y \) on the left-hand side is conventionally replaced with \( f(x) \) to indicate that \( y \) is a function of \( x \). Thus,
[tex]\[ f(x) = 6x + 9 \][/tex]
4. Compare with the given options to find the correct answer:
- Option 1: \( f(x) = 6x + 9 \)
- Option 2: \( f(x) = \frac{1}{6}x + \frac{3}{2} \)
- Option 3: \( f(y) = 6y + 9 \)
- Option 4: \( f(y) = \frac{1}{6}y + \frac{3}{2} \)
From our steps, we see that the equation \( f(x) = 6x + 9 \) matches Option 1.
Therefore, the correct answer is:
[tex]\[ f(x) = 6x + 9 \][/tex]
Hence, the correct option is:
[tex]\[ 1 \][/tex]
1. Given equation: \( y - 6x - 9 = 0 \).
2. Isolate \( y \) in terms of \( x \):
[tex]\[ y = 6x + 9 \][/tex]
3. Rewrite this equation in function notation:
The variable \( y \) on the left-hand side is conventionally replaced with \( f(x) \) to indicate that \( y \) is a function of \( x \). Thus,
[tex]\[ f(x) = 6x + 9 \][/tex]
4. Compare with the given options to find the correct answer:
- Option 1: \( f(x) = 6x + 9 \)
- Option 2: \( f(x) = \frac{1}{6}x + \frac{3}{2} \)
- Option 3: \( f(y) = 6y + 9 \)
- Option 4: \( f(y) = \frac{1}{6}y + \frac{3}{2} \)
From our steps, we see that the equation \( f(x) = 6x + 9 \) matches Option 1.
Therefore, the correct answer is:
[tex]\[ f(x) = 6x + 9 \][/tex]
Hence, the correct option is:
[tex]\[ 1 \][/tex]
