Question

5. Choose if the following relations are functions or not functions.
{(1,3), (2,3), (-8,3), (0,3)} is _____________
{(4,9), (-3,1), (6,3), (4,3), (7,14)} is ___________
not a Function
{(3,2.5), (8, -1.4), (4.5, -10), (3,2.5), (1.2,1.8)} is __________
{(0,0), (-1,1), (-2,2), (-3,3), (-4,4)} is _________

A) a Function
B) not a Function

Answer 1

To determine if the given sets of pairs are functions, we need to check if each input (first element of the pair) maps to exactly one output (second element of the pair). If any input maps to more than one output, it is **not a function**.

1. {(1,3), (2,3), (-8,3), (0,3)} - Here, every input (1, 2, -8, 0) maps to the output 3. Therefore, this is **A) a Function**.

2. {(4,9), (-3,1), (6,3), (4,3), (7,14)} - Here, the input 4 maps to two different outputs (9 and 3). Therefore, this is **B) not a Function**.

3. {(3,2.5), (8,-1.4), (4.5,-10), (3,2.5)} - The input 3 maps to the output 2.5 but is listed twice. Since each input must map to exactly one output, it still qualifies as a function. Therefore, this is **A) a Function**.

4. {(0,0), (-1,1), (-2,2), (-3,3), (-4,4)} - Here, every input maps to a unique output. Therefore, this is **A) a Function**.

In summary:
1. a Function
2. not a Function
3. a Function
4. a Function