Question

1. (12 points) for each graph below, determine whether it represents a function. circle the appropriate response below each graph.

graph 1:
function? yes no

graph 2:
function? yes no

graph 3:
function? yes no

graph 4:
function? yes no

graph 5:
function? yes no

graph 6:
function? yes no

Explanation:

Step 1: Analyze Row 1, Graph 1

A vertical line intersects the curve multiple times.

$$\text{Function? No}$$

Step 2: Analyze Row 1, Graph 2

Two points share the same x-coordinate at \(x = -3\).

$$\text{Function? No}$$

Step 3: Analyze Row 1, Graph 3

Every vertical line intersects the curve at most once.

$$\text{Function? Yes}$$

Step 4: Analyze Row 2, Graph 1

The open and closed endpoints prevent overlapping x-values.

$$\text{Function? Yes}$$

Step 5: Analyze Row 2, Graph 2

A vertical line at \(x = -1\) intersects two points.

$$\text{Function? No}$$

Step 6: Analyze Row 2, Graph 3

A vertical line intersects the parabola twice.

$$\text{Function? No}$$

Answer:

Row 1, Graph 1: No
Row 1, Graph 2: No
Row 1, Graph 3: Yes
Row 2, Graph 1: Yes
Row 2, Graph 2: No
Row 2, Graph 3: No