Which relation is NOT a function?
Y=0
X=2
Y=2x
Y=x+2
x=2 is a vertical line, thus not a function
the others are non-vertical lines
All non-vertical straight lines are functions.
The relation that is NOT a function is Y=2x.
To determine which relation is not a function, we need to check if there are any inputs (x-values) that correspond to multiple outputs (y-values).
Let's go through each relation and analyze them:
1. Y = 0
Since the value of y is always 0, there is no variability in the output for any given input. Therefore, this relation is a function.
2. X = 2
In this relation, the value of x is fixed at 2. For every input (x-value) of 2, there is a consistent output (y-value). Thus, this relation is also a function.
3. Y = 2x
This relation represents a linear equation where the output (y-value) is twice the input (x-value). For example, when x = 1, y = 2; when x = 2, y = 4, and so on. Since every input has a unique output, this relation is a function.
4. Y = x + 2
In this relation, the output (y-value) is obtained by adding a constant of 2 to the input (x-value). For instance, when x = 1, y = 3; when x = 2, y = 4, and so on. Just like the previous relations, each input has a distinct output, so this relation is also a function.
Therefore, out of the given relations, there are no relations that are not functions.