Answer:
The given relation is not a function.
Step-by-step explanation:
Given the relation: {(3,2) (8,16) (13,8) (14,14) (20,5) (24,8) (27,2) (31,6) (31,3)}
A relation is any set of ordered pairs, which can be thought of as (input, output).
A function is a relation in which no two ordered pairs have the same first component (x-values or input) and different second components (y-values or output).
- We need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)?
- In this case, the answer is no. The input value (x = 31) goes with two output values, 6 and 3.
- It only takes one input or x-value to associate with more than one output value to be invalid as a function.
Another way to find out whether a relation or a set of given points represent a function through the Vertical Line Test. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
To use the vertical-line test, imagine dragging a ruler held vertically across the graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value. If you do this for the given set of points, every vertical line intersects the graph in at most one point, except for the x-value = 31, where the vertical line contains two points (in red dots) in it: (31,6) and (31,3). The given graph fails the Vertical Line Test, which means that it is not a function.
Attached is a screenshot of the graph where I performed the Vertical Line Test.
Please mark my answers as the Brainliest if you find my explanation helpful :)
