From the diagrams above, select one of them which best illustrates each of the following statements.

1. Match the cubic function to its graph shape

$y=4\pi x^3$ is of the form $y=ax^n$, where $a>0$ and $n=3$.

For positive $x$, $y$ increases from the origin and rises more steeply as $x$ increases. This matches the increasing curve through the origin in Diagram 4.

1. Match the cost model to the correct graph shape

Since $y$ is a linear function of $x$, the graph is a straight line.

The fixed cost is $100, so when $x=0$, $y=100$. Hence the graph has a positive $y$-intercept and increases as the number of man-hours increases.

This matches Diagram 3.

1. Identify the correct graph shape from the motion described

The object travels at a constant speed towards point O, so its distance $y$ from O decreases at a constant rate as time $x$ increases.

Hence the graph of $y$ against $x$ is a straight line with negative gradient. This matches Diagram 2.