2. What is g(6)and what does it represent in the context of this example?

g(x) = 30

Step-by-step explanation:

Let the function representing line in graph 2 is,

g(x) = mx + b

Here m = slope of the line

b = y-intercept

Since the given line passes through origin (0, 0), y-intercept of the function will be 0.

Slope of the line =

                           =

                           = 5

Therefore, function will be g(x) = 5x

For x = 6,

g(6) = 30

This function represents that height of liquid in the cylinder is directly proportional to the amount of liquid poured in the cylinder.

(0, 12)
f(x) = (x-6)(x-2) 
(Multiply or foil)... x(x-6) -2(x-6) = x^2 - 6x - 2x + 12 = x^2 -8x + 12.
So we have, f(x) = x^2 -8x + 12(in the form, ax^2 + bx + c c is the y-intercept ... so, 12)
the y-intercept is where the graph intercepts the y-axis, meaning x=0.
f(0) = (0)^2 - (0)x +12 = 12 (0, 12)