Question
Graph the relation {(5, 0), (0, 5), (5, 1), (1, 5)}. Is it a function? Why or why not?
No, it does not pass the horizontal-line test.
Yes, it passes the vertical-line test.
No, it does not pass the vertical-line test.
Yes, it passes the horizontal-line test.
No, it does not pass the horizontal-line test.
Yes, it passes the vertical-line test.
No, it does not pass the vertical-line test.
Yes, it passes the horizontal-line test.
Answers
GPT-4o mini
To determine if the given relation \(\{(5, 0), (0, 5), (5, 1), (1, 5)\}\) is a function, we need to apply the definition of a function: each input (or x-value) must correspond to exactly one output (or y-value).
Let's evaluate the x-values in the relation:
- The point \((5, 0)\) has an x-value of 5.
- The point \((0, 5)\) has an x-value of 0.
- The point \((5, 1)\) also has an x-value of 5.
- The point \((1, 5)\) has an x-value of 1.
Here, we see that the x-value of 5 corresponds to two different y-values: 0 and 1. Because of this, the input 5 does not have a unique output.
Therefore, the relation does not satisfy the criteria of a function.
### Conclusion:
**No, it does not pass the vertical-line test.**
In a graphical sense, if we were to plot these points, drawing a vertical line at \(x = 5\) would intersect the graph at two points, which confirms that it is not a function.
Let's evaluate the x-values in the relation:
- The point \((5, 0)\) has an x-value of 5.
- The point \((0, 5)\) has an x-value of 0.
- The point \((5, 1)\) also has an x-value of 5.
- The point \((1, 5)\) has an x-value of 1.
Here, we see that the x-value of 5 corresponds to two different y-values: 0 and 1. Because of this, the input 5 does not have a unique output.
Therefore, the relation does not satisfy the criteria of a function.
### Conclusion:
**No, it does not pass the vertical-line test.**
In a graphical sense, if we were to plot these points, drawing a vertical line at \(x = 5\) would intersect the graph at two points, which confirms that it is not a function.