Name: Understanding Functions
Uploaded: 2019-07-19
Duration: 12 min 27 s
Description: A function is a machine that relates an input to an output. Functions have applications in algebra, calculus, science, etc. Watch this video.

Question

Use the vertical line test to determine whether the following graph is a function or not. Explain your answer.

Accepted Answer

Given graph is

We know that a relation is defined as a function when there is exactly one output value ' $y$ ' for each input value ' $x$ ', and if there are multiple values of $y$ for an $x$ value then the relation will not be a function.

Now, we will use the vertical line test to find whether the relation is a function or not.

For that we will draw a vertical line cutting through the graph of the relation, and then observe the points of intersection.

If the vertical line intersects the graph more than once this suggests that a single $x$ -value is being associated with more than one value of $y$ . And, in that case the given relation will not be a function, whereas If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

Thus, drawing the vertical line in the given graph, we have

Here, if we see that the vertical line drawn parallel to $y$ -axis intersects the graph at exactly one point.

Thus, it passes the vertical line test, and the given graph represents a function.

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