2.4.1 Ellipse Relation Domain & Range

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 2.4 Domain, Range, & More

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Ellipse Relation Domain & Range

$E = {(x, y) \in R \times R : \frac{x^{2}}{256} + \frac{y^{2}}{25} \leq 1}$

is a disc whose bounding is an ellipse.

left=-16; right=16;
top=10; bottom=-10;
height=300; width=500;
---
\frac{x^{2}}{256}+\frac{y^{2}}{25}\le1

Solution. From the graph, we see an ellipse. Moreover, we can find:

\begin{aligned} Domain Space (E) & = R \\ Dom (D) & = [- 16, 16] \subset R \\ Codom (E) & = R \\ Rng (E) & = [- 5, 5] \subset R \end{aligned}