Question

consider the following.
graph of a vertical ellipse centered at (0,0) with y-intercepts at (0,4) and (0,-4), and x-intercepts at (-1,0) and (1,0) (approximate)
use the vertical line test to determine whether the curve is the graph of a function of x.
∘ yes, the curve is a function of x.
∘ no, the curve is not a function of x.
if the curve is a function, state the domain and range. (enter your answers using interval notation. if...
domain
range

Explanation:

Step1: Recall Vertical Line Test

The Vertical Line Test states that a graph represents a function of \( x \) if and only if no vertical line intersects the graph more than once.

Step2: Apply the Test to the Graph

Looking at the given graph (an ellipse), if we draw a vertical line (e.g., \( x = 0 \) or any vertical line within the domain of the ellipse), it will intersect the ellipse at two points. This means there are \( x \)-values that correspond to more than one \( y \)-value.

Step3: Conclusion from the Test

Since a vertical line intersects the graph at more than one point, the curve does not pass the Vertical Line Test. Therefore, the curve is not a function of \( x \).

Answer:

No, the curve is not a function of \( x \).