Question

six graphs are shown below. click on the tabs to see them.
graph 1 graph 2 graph 3 graph 4 graph 5 graph 6
check the box corresponding to each graph that represents a function.
☑ graph 1 ☑ graph 2 ☐ graph 3 ☐ graph 4 ☐ graph 5 ☐ graph 6 ☐ none of the graphs

Explanation:

To determine if a graph represents a function, we use the vertical line test: a graph is a function if no vertical line intersects it more than once.

Analyzing Graph 4:

1. Identify the coordinates of the points (from the grid):

• Left - most point: Let’s assume the grid has 1 unit per square. The left - most point seems to be at \((-3, -5)\) (x = - 3, y = - 5).
• Next: \((-1, 0)\) (x=-1, y = 0).
• Then: \((1, -2)\) (x = 1, y=-2).
• Then: \((3, -5)\) (x = 3, y=-5).
• Then: \((5, -4)\) (x = 5, y=-4).

1. Apply the vertical line test:

For any vertical line \(x = a\) (where \(a\) is a real number), we check how many times it intersects the graph. Since each \(x\) - value ( - 3, - 1, 1, 3, 5) has only one corresponding \(y\) - value, no vertical line will intersect the graph more than once. Thus, Graph 4 does represent a function and should have its box checked.

Correcting the Selection:

The initial selection was incorrect for Graph 4. The correct selection should include Graph 4 (along with Graph 1 and Graph 2, assuming they also pass the vertical line test). If we only focus on Graph 4:

Graph 4 passes the vertical line test (each \(x\) - value has one \(y\) - value), so it represents a function.

Answer:

Graph 4 (the box next to Graph 4 should be checked).