Consider the function represented by the equation 6q = 3s - 9. Write the equation in function notation, where q is the independent variable.

Answer 1

In general, with the Dependent variable is the only item on the right side of the equation, making the Independent variable on the right with coefficients and constants (intercepts).

ex. 4x+5 = y ; x is independent, y is dependent.

to make a function of x, we switch it around

f(x) = 4x+5

Solution:

6q = 3s - 9 (original)

6q + 9 = 3s - 9 + 9 = 3s ( adding 9 to both sides leaves just 3s on the right)

(6q + 9)/3 = 3s/3 = s (divide both sides by 3 to get the dependent variable on right with out coefficients)

(6q + 9)/3 = 2q +3 = s

2q +3 = s = f(q) (replace s with f(q) for function notation)

Answer: f(q) = 2q + 3