I've been stuck on this question for awhile.
"A relation contains the points (-5,-10), (-2,-4), (-1,-2), (4,80) and (5,10). Is this a function? Explain."
To determine if the given relation is a function, we need to check if each input value (x-coordinate) is associated with a unique output value (y-coordinate). Here are the steps to determine if the relation is a function:
Step 1: List all the x-coordinates (input values):
x-coordinates: -5, -2, -1, 4, 5
Step 2: List all the y-coordinates (output values):
y-coordinates: -10, -4, -2, 80, 10
Step 3: Check if each x-coordinate has a unique y-coordinate. In other words, if any x-coordinate is associated with more than one y-coordinate, the relation is not a function.
In this case, let's examine each x-coordinate:
For x = -5, the corresponding y-coordinate is -10.
For x = -2, the corresponding y-coordinate is -4.
For x = -1, the corresponding y-coordinate is -2.
For x = 4, the corresponding y-coordinate is 80.
For x = 5, the corresponding y-coordinate is 10.
As we can see, each x-coordinate is associated with only one y-coordinate, and there are no repeated x-coordinates. Therefore, the relation is a function.
In conclusion, the given relation is a function because each x-coordinate is associated with a unique y-coordinate.
To determine if the given relation is a function, we need to check if each input (x-value) is associated with only one output (y-value). Here's how we can go about solving this:
1. Identify the given set of points: (-5,-10), (-2,-4), (-1,-2), (4,80), and (5,10).
2. Take note of the x-values in the relation: -5, -2, -1, 4, and 5.
3. Check if any of the x-values repeat in the relation. In this case, there are no repeating x-values.
4. Now, examine the y-values corresponding to each x-value: -10, -4, -2, 80, and 10.
5. Notice that each x-value is associated with a unique y-value. There are no repeating y-values for any of the x-values.
6. Since each input (x-value) is paired with only one output (y-value) without any repetition, we can conclude that this relation is indeed a function.
In summary, this relation is a function because every input (x-value) corresponds to exactly one output (y-value) without any repetition.