Which table represents a function?
x|3|-1|1|-1
y|0|4|2|-2
________
x|0|1|0|2
y|2|3|0|3
_______
x|-2|2|4|-2
y|5|1|5|5
_______
x|5|4|5|1
y|1|5|4|5
I am not sure how to know. So please explain so next time I can know how :).
To determine which table represents a function, we need to understand what a function is. A function is a relation where each input value (x) corresponds to exactly one output value (y). In other words, for each x-value, there should be only one corresponding y-value.
To find out if a table represents a function, we can look for any repeated x-values with different y-values. If there are any x-values that have multiple y-values, then the table does not represent a function.
Let's go through each table to determine if they represent a function:
1. Table 1:
x|3|-1|1|-1
y|0|4|2|-2
In this table, we notice that the x-value -1 has two corresponding y-values, 2 and -2. This means that for the input value of -1, there are two possible output values, violating the definition of a function. Therefore, Table 1 does not represent a function.
2. Table 2:
x|0|1|0|2
y|2|3|0|3
In this table, the different x-values each have unique corresponding y-values. There are no repeated x-values with different y-values. Therefore, Table 2 represents a function.
3. Table 3:
x|-2|2|4|-2
y|5|1|5|5
In this table, the x-value -2 has two corresponding y-values, 5 and 5. This means that for the input value of -2, there are two possible output values, which violates the definition of a function. Therefore, Table 3 does not represent a function.
4. Table 4:
x|5|4|5|1
y|1|5|4|5
In this table, the different x-values each have unique corresponding y-values. There are no repeated x-values with different y-values. Therefore, Table 4 represents a function.
So, based on our analysis, Table 2 and Table 4 represent functions, while Table 1 and Table 3 do not represent functions.