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)

Explanation:

Step1: Use vertical - line test

If a vertical line intersects the graph at most once, it is a function. If it intersects more than once, it is not a function.

Step2: Use horizontal - line test for one - to - one

If a horizontal line intersects the graph of a function at most once, the function is one - to - one.

First graph (V - shaped):

It passes the vertical - line test (any vertical line intersects at most once), and fails the horizontal - line test (a horizontal line above the vertex intersects twice). So it is a function, but not one - to - one.

Second graph (discrete points):

It passes the vertical - line test (no two points have the same x - coordinate), and passes the horizontal - line test (no two points have the same y - coordinate). So it is a one - to - one function.

Third graph (curved):

It passes the vertical - line test (any vertical line intersects at most once) and passes the horizontal - line test (any horizontal line intersects at most once). So it is a one - to - one function.

Fourth graph (circle):

It fails the vertical - line test (a vertical line through the center of the circle intersects twice). So it is not a function.

Answer:

1. First graph: a) a function, but not one - to - one
2. Second graph: b) one - to - one function
3. Third graph: b) one - to - one function
4. Fourth graph: c) not a function