Final answer:
The volume V of the cylinder can be represented as a function of x using the formula V = π(48x² - 36x + 16).
Step-by-step explanation:
The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, the radius of the cylinder is 4x - 2 and the height is 4 - 3x. To find the volume as a function of x, we substitute these expressions into the formula:
V = π(4x - 2)²(4 - 3x)
Simplifying further, we have:
V = π(16x² - 16x + 4)(4 - 3x)
V = π(64x² - 48x - 16x² + 12x + 16)
V = π(48x² - 36x + 16)
This is the volume of the cylinder as a function of x. The corresponding graph would have x as the independent variable and the volume as the dependent variable.