Identity whether the given relation is a Function or Not.
If Relation alone = write R
If it is a Function = write F
1. Ordered pairs (x,y)
1,2),(3,5),(5,-2),(3,6),(10,15),(7,0)
2. A parabola opening to the right
3. A circle
4. A line sloping upward right
5. The relation described by the equation y=/x/
6. The relation described by the equation y²=5x-3y
7. An ellipse
8. A parabola opening downward
9. Ordered pairs (x,y)
1,3),(2,3),(5,3),(-12,3)
10. The relation described by the equation y=√x+5
To determine whether each given relation is a function or not, we need to check if each input (x-value) is associated with only one output (y-value).
1. Ordered pairs (x,y): (1,2),(3,5),(5,-2),(3,6),(10,15),(7,0)
- This is a function (F) because each x-value is associated with only one y-value.
2. A parabola opening to the right
- This is not a function (R) because for a given x-value, there can be multiple y-values.
3. A circle
- This is not a function (R) because for a given x-value, there can be multiple y-values.
4. A line sloping upward right
- This is a function (F) because each x-value is associated with only one y-value.
5. The relation described by the equation y = |x|
- This is a function (F) because each x-value is associated with only one y-value.
6. The relation described by the equation y² = 5x - 3y
- This is not a function (R) because for a given x-value, there can be multiple y-values.
7. An ellipse
- This is not a function (R) because for a given x-value, there can be multiple y-values.
8. A parabola opening downward
- This is not a function (R) because for a given x-value, there can be multiple y-values.
9. Ordered pairs (x,y): (1,3),(2,3),(5,3),(-12,3)
- This is a function (F) because each x-value is associated with only one y-value.
10. The relation described by the equation y = √x + 5
- This is a function (F) because each x-value is associated with only one y-value.
In summary:
1. F
2. R
3. R
4. F
5. F
6. R
7. R
8. R
9. F
10. F