you can inspect whether a graph represents a role by using the vertical line test.

The test states that a graph to represent a duty if and also only if every vertical lines crossing the graph at many once.

example :

 This graph walk not represent a function: for example, the vertical heat x = 1 intersects the in three places. This graph does represent a function, due to the fact that any type of vertical line intersects the graph precisely once, other than x = 0 , which doesn"t crossing it in ~ all.

take into consideration the graph shown.

You deserve to see that no vertical lines pass with two points on the graph.

keep in mind that ( − 2 , 0 ) and also ( 1 , − 2 ) are open points and are no on the graph. So, the vertical lines x = − 2 and also x = 1 pass through just one point on every of the line segments.

Therefore, the graph shown is the a function.

The step role can be defined as:

y = 1 2 x + 1 y = − x − 1 y = 5 − 6 ≤ x − 2 − 2 ≤ x 1       1 ≤ x ≤ 6

The domain the the role is − 6 ≤ x ≤ 6 and the range is − 2 ≤ y ≤ 5 .

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