Question

1. (0 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:

Step1: Apply vertical line test to Graph 1

No vertical line intersects more than one point.

$$\text{Function: Yes}$$

Step2: Apply vertical line test to Graph 2

A vertical line intersects the curve multiple times.

$$\text{Function: No}$$

Step3: Apply vertical line test to Graph 3

Every vertical line intersects the parabola at most once.

$$\text{Function: Yes}$$

Step4: Apply vertical line test to Graph 4

A vertical line near the vertex intersects two segments.

$$\text{Function: No}$$

Step5: Apply vertical line test to Graph 5

At \(x = 0\), there is one closed and one open circle.

$$\text{Function: Yes}$$

Step6: Apply vertical line test to Graph 6

At \(x = 0\), there are two closed circles.

$$\text{Function: No}$$

Answer:

Row 1, Graph 1 (discrete points): Yes
Row 1, Graph 2 (vertical wave): No
Row 1, Graph 3 (parabola): Yes
Row 2, Graph 1 (sideways V-shape): No
Row 2, Graph 2 (piecewise with open/closed circles): Yes
Row 2, Graph 3 (piecewise with overlapping closed circles): No