Question

The table shows a familiar pattern from geometry. Determine what the variables $\mathrm{x}$ and $\mathrm{y}$ represent. Then write a function rule that relates $\mathrm{y}$ to $\mathrm{x}$.

Answer 1

From the above table ordered pairs are $(1,\mathrm{\pi })(2,2\mathrm{\pi })(3,3\mathrm{\pi })(4,4\mathrm{\pi })(5,5\mathrm{\pi })$.

Here, $\mathrm{x}$ is is diameter of circle and $\mathrm{y}$ is the circumference.

We know, circumference of circle $\mathrm{y}=\mathrm{\pi d}$ where, diameter $\mathrm{d}=\mathrm{x}$ given.

Thus, function rule: $\mathrm{y}=\mathrm{\pi x}$

Hence, a function rule that relates $\mathrm{y}$ to $\mathrm{x}$ is $\mathrm{y}=\mathrm{\pi x}$.