Question

consider the function represented by the equation 6q = 3s - 9. write the equation in function notation, where q is the independent variable.\
\\(\bigcirc\\) \\(f(q) = \frac{1}{2}q - \frac{3}{2}\\)\
\\(\bigcirc\\) \\(f(q) = 2s + 3\\)\
\\(\bigcirc\\) \\(f(s) = \frac{1}{2}s - \frac{3}{2}\\)\
\\(\bigcirc\\) \\(f(q) = 2q + 3\\)

Explanation:

Step1: Isolate $s$ term

Start with the given equation:
$$6q = 3s - 9$$
Add 9 to both sides:
$$6q + 9 = 3s$$

Step2: Solve for $s$

Divide all terms by 3:
$$s = \frac{6q}{3} + \frac{9}{3}$$
Simplify the fractions:
$$s = 2q + 3$$

Step3: Write in function notation

Since $q$ is the independent variable, define $f(q)=s$:
$$f(q) = 2q + 3$$

Answer:

D. $f(q) = 2q + 3$