Mastering the Vertical Line Test for Functions

The video tutorial explains the vertical line test, a method to determine if a relation is a function. It demonstrates how to apply the test to various graphs, showing examples where the test is passed or failed. The test states that if a vertical line intersects a graph at more than one point, the relation is not a function. The tutorial includes examples with holes, points, and coordinate planes to illustrate the concept.

What does the Vertical Line Test determine?

• If a graph has an asymptote

• If a graph is a straight line

• If a relation is a function

• If a graph is horizontal

What is the result if a vertical line intersects a graph at more than one point?

• The graph is a circle

• The graph is a straight line

• The graph is a function

• The graph is not a function

In the first example, why is the graph considered a function?

• Vertical lines intersect the graph at exactly one point

• It has no vertical lines

• It is a straight line

• It has multiple outputs for each input

Why does the second graph fail the Vertical Line Test?

• It has only one output for each input

• It is a straight line

• Vertical lines intersect the graph at two points

• It has no vertical lines

What happens when x = 5 in the second graph?

• There is one corresponding y value

• The graph is undefined

• There are two corresponding y values

• There are no corresponding y values

How does the presence of a hole and a point at x = 2 affect the Vertical Line Test?

• It passes the test

• It makes the graph undefined

• It creates multiple outputs

• It fails the test

What is the result of the Vertical Line Test on a graph with points on the coordinate plane?

• It depends on the number of points

• It always passes

• It depends on the position of points

• It always fails

Why does the graph with x = 4 fail the Vertical Line Test?

• It has no vertical lines

• Vertical lines intersect the graph at two points

• It is a straight line

• It has only one output for each input

What is the significance of a break in the graph at x = 0?

• It fails the test

• It creates multiple outputs

• It makes the graph undefined

• It passes the test

What is the result of the Vertical Line Test on the final graph with x = -1?

• It has no points of intersection

• It is undefined

• It fails the test

• It passes the test