Final answer:
The function f(x) = 3x - 7 can be stretched vertically by a factor of 4 and translated up by 9 units to obtain the function g(x) = 12x - 19.
Step-by-step explanation:
The function f(x) = 3x - 7 stretched vertically by a factor of 4 and translated up by 9 units can be represented as:
g(x) = 4(3x - 7) + 9
First, apply the vertical stretch by multiplying the function by 4: g(x) = 12x - 28. Then, apply the vertical translation by adding 9 to the y-values: g(x) = 12x - 28 + 9 = 12x - 19.
So, the function g(x) = 12x - 19 represents the stretched and translated version of f(x).