Question

1. Mark each of the following graphs as (a) a function, but not one-to-one, (b) one-to-one function, or (c) not a function. In each case, explain how you know. (1 point each)​

Answer 1

(a) a function, but not one-to-one

Explanation:

The graph is of a function if it passes the vertical line test: a vertical line intersects the graph in at most 1 point.

The function is one-to-one if it passes the horizontal line test: a horizontal line intersects the graph in at most 1 point.

__

Here, the graph consists of a series of non-overlapping horizontal lines. It passes the vertical line test (is a function), but a horizontal line can intersect the graph in an infinite number of points (is not one-to-one).

The graph is a function, but not one-to-one.