Question

1. consider the circular relation on the graph below. 8a what is the domain of the relation? express your answer using inequalities.

Explanation:

Step1: Identify the center and radius

The center of the circle is at the origin $(0,0)$ and the radius $r = 3$ (by counting the grid - units from the center to the circle).

Step2: Recall the domain formula for a circle

For a circle centered at the origin with radius $r$, the domain is given by the $x$ - values that the circle covers. The equation of a circle is $x^{2}+y^{2}=r^{2}$. Solving for $x$ gives $x=\pm\sqrt{r^{2}-y^{2}}$. The left - most and right - most $x$ values occur when $y = 0$.

Step3: Determine the domain

When $y = 0$, $x=\pm r$. Since $r = 3$, the domain of the relation (the set of all possible $x$ values) is $- 3\leqslant x\leqslant3$.

Answer:

$-3\leqslant x\leqslant3$