Explain how you would determine wether each of the following represents a function:
Set of ordered pairs-
Mapping diagram-
Graph-
To determine whether each of the following represents a function, you need to understand what a function is and examine the given representations.
A function is a relation where each input (or x-value) has only one output (or y-value). In other words, for every element in the domain (x-value), there can only be one corresponding element in the range (y-value).
1. Set of ordered pairs:
To determine if a set of ordered pairs represents a function, you need to examine the x-values and check if each x-value has a unique y-value. If there is any x-value that repeats with different y-values, the set does not represent a function.
For example, if you have the following set of ordered pairs:
{(1, 2), (2, 3), (1, 4)}
In this case, the x-value 1 repeats with two different y-values (2 and 4), so it does not represent a function.
2. Mapping diagram:
A mapping diagram visually represents a function, showing the relationship between the elements in the domain and the elements in the range. To determine if the mapping diagram represents a function, you need to check if each element in the domain maps to exactly one element in the range. If any element in the domain maps to multiple elements in the range, the mapping diagram does not represent a function.
For example, if you have the following mapping diagram:
A -> 1
B -> 2
C -> 1
D -> 3
In this case, both element A and C in the domain map to the same element (1) in the range. Therefore, the mapping diagram does not represent a function.
3. Graph:
To determine if a graph represents a function, you need to examine if there are any vertical lines that intersect the graph at more than one point. If there are no such lines, then the graph represents a function.
For example, if you have a graph that passes the vertical line test, where no vertical line intersects the graph at more than one point, then the graph represents a function.
In conclusion, to determine whether each representation (set of ordered pairs, mapping diagram, or graph) represents a function, you need to analyze if each input (x-value) corresponds to only one output (y-value).