Question

six graphs are shown below. click on the tabs to see them.
graph 1 graph 2 graph 3 graph 4 graph 5
(graph 4s coordinate plane graph is shown)
check the box corresponding to each graph that represents a function.
☑️ graph 1 ☐ graph 2 ☑️ graph 3 ☐ graph 4 ☐ graph 5 ☐ graph 6

Explanation:

Step1: Recall the vertical line test

A graph represents a function if and only if no vertical line intersects the graph more than once.

Step2: Analyze Graph 4

Looking at Graph 4, which is a parabola opening upwards with vertex at the origin \((0,0)\). If we draw any vertical line \(x = a\) (where \(a\) is a real number), it will intersect the parabola at most once. So Graph 4 passes the vertical line test.

Answer:

We should check the box for Graph 4. So the correct option is:
\(\boldsymbol{\square}\) Graph 1 (already checked, but for Graph 4: \(\boldsymbol{\checkmark}\) Graph 4, \(\square\) Graph 2, \(\boldsymbol{\checkmark}\) Graph 3 (already checked), \(\boldsymbol{\checkmark}\) Graph 4 (now checked), \(\square\) Graph 5, \(\square\) Graph 6)

(Note: The initial checks for Graph 1 and Graph 3 seem correct as they likely pass the vertical line test, and now Graph 4 also passes. The user's initial check for Graph 4 was wrong; it should be checked as it represents a function.)