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.
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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