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Consider the function represented by the equation [tex]y - 6x - 9 = 0[/tex]. Which answer shows the equation written in function notation with [tex]x[/tex] as the independent variable?

A. [tex]f(x) = 6x + 9[/tex]

B. [tex]f(x) = \frac{1}{6}x + \frac{3}{2}[/tex]

C. [tex]f(y) = 6y + 9[/tex]

D. [tex]f(V) = \frac{1}{6}V - 3[/tex]


Sagot :

To rewrite the equation [tex]\(y - 6x - 9 = 0\)[/tex] in function notation with [tex]\(x\)[/tex] as the independent variable, we need to express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].

1. Start with the given equation:
[tex]\[ y - 6x - 9 = 0 \][/tex]

2. Move the term involving [tex]\(x\)[/tex] and the constant to the other side of the equation by adding [tex]\(6x\)[/tex] and [tex]\(9\)[/tex] to both sides:
[tex]\[ y = 6x + 9 \][/tex]

3. The equation [tex]\(y = 6x + 9\)[/tex] expresses [tex]\(y\)[/tex] as a function of [tex]\(x\)[/tex].

4. In function notation, this is typically written as:
[tex]\[ f(x) = 6x + 9 \][/tex]

5. Reviewing the provided options, the equation written in function notation, with [tex]\(x\)[/tex] as the independent variable, is:
[tex]\[ f(x) = 6x + 9 \][/tex]

Therefore, the correct answer is:
[tex]\[ f(x) = 6x + 9 \][/tex]
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