Question

determine if a graph is a function.

is this the graph of a function?

yes
no

Explanation:

Identify the given graph

The graph shown is an ellipse centered at approximately \((-1, 0)\) with a horizontal semi-axis of \(4\) units and a vertical semi-axis of \(3\) units.

Apply the vertical line test

To determine if a graph represents a function, we use the vertical line test. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Analyze intersections

For many vertical lines (for example, the y-axis \(x = 0\)), the line crosses the ellipse at two distinct points: one in the upper half and one in the lower half.

Conclude function status

Because a single input \(x\) maps to multiple outputs \(y\), this relation does not define \(y\) as a function of \(x\).

Answer:

• Yes
• No (Correct answer)