Question

1. tell whether each of the following graphs is a function and explain your reasoning.

a. graph a
b. graph b

Explanation:

For graph a: Use the Vertical Line Test—any vertical line drawn on the graph intersects the curve at more than one point. A function requires each input (x-value) to have exactly one output (y-value), so this fails the test.
For graph b: Use the Vertical Line Test—every vertical line drawn on the graph intersects the curve at exactly one point. This satisfies the definition of a function, where each x-value has only one corresponding y-value.

Answer:

a. This graph is NOT a function. It fails the Vertical Line Test, as some x-values correspond to multiple y-values.
b. This graph IS a function. It passes the Vertical Line Test, as every x-value has exactly one corresponding y-value.