Question

1. (12 points) for each function graphed below, determine whether it is 1-1. circle the appropriate response below each graph.

graph 1:
one-to-one? yes no

graph 2:
one-to-one? yes no

graph 3:
one-to-one? yes no

Explanation:

Step 1: Analyze the first graph

Apply the horizontal line test to the first graph.

$$ y = 1 \text{ intersects the graph at two distinct points.} $$

Step 2: Analyze the second graph

Apply the horizontal line test to the second graph.

$$ \text{Every horizontal line intersects the graph at most once.} $$

Step 3: Analyze the third graph

Apply the horizontal line test to the discrete points.

$$ \text{No two points share the same } y\text{-coordinate.} $$

Answer:

First graph: No
Second graph: Yes
Third graph: Yes