Question

Use the vertical line test and select the graphs below in which represent y as a function of x.

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Answer 1

A and C (read below to see which ones are A and C.

Explanation:

A: (upper left) a function. If you put a ruler on any x value, you will hit just 1 y no matter where you place the ruler.

B: (upper right) not a function. If you place the ruler on x = -2 you get 3 y values. definitely not a function.

C: lower left. That looks like a function. Hard to tell what is going on the left.

D: A circle is never a function. Many x values have 2 y values. Can't do and still call it a function

Answer 2

Graphs 1 and 3 are functions.

Explanation:

A curve in the xy-plane is a function if and only if no vertical line intersects the curve more than once. The Vertical Line Test allows us to know whether or not a graph is actually a function. Remember that a function can only take on one output for each input.

In the attached image, I've conducted the Vertical Line Test to demonstrate which are the graphs that represent y as a function of x.

The 1st and 3rd graphs (left-hand side graphs) represent a function because each vertical line drawn crosses those curves at most once.

The 2nd and 4th graph do not represent a function because, at most x-values, a vertical line would intersect the graph at more than one point.