Question

Use the vertical-line test to determine which graph represents a function.

Answer 1

Answer:  Choice C

This is the flat horizontal graph

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Explanation:

If it is possible to pass 1 single vertical line through more than one point on the curve, then that curve is not a function. It is said that the curve fails the vertical line test in this case.

Choice A, B and D are examples of this.

In each of these graphs, we have an input that leads to multiple outputs.

Rule: A function has one output for any given input

Put another way, one input and one output.

The inputs in question must be in the domain.

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In choice C, we have any given x input lead to exactly one y output. The graph passes the vertical line test since it's impossible to pass a single vertical line through more than one point on this graph.

This is why choice C is the answer, which is the flat horizontal graph.

Answer 2

Answer:

The third picture represents a function.

Step-by-step explanation:

The vertical line test is basically making sure that two points do not have the same x-coordinate. In the first graph, the two lines share the same x-coordinates on each point, therefore, it is not a function.

The second picture is a vertical line, and functions cannot be a vertical line, therefore it isnt a function.

In the fourth picture, several points have the same x-coordinate as well.

If you still dont understand the vertical line test, heres an example from the fourth picture:

Point (-2,2) and Point (-2,-2) are both points that fall on the curve. They both have the same x-coordinate, -2. Because of this, the graph cannot be a function. Several other points on the graph also share a same x-coordinate.

Hope this makes sense and helps :)