Question

name: 6.1 function: yes or no? 1. determine if the following is a function. {(1, -1), (2, -2), (3, -3), (4, -4)} circle: yes or no why? 2. determine if the following is a function. {(1, 3), (1, 0), (1, -2), (1, 8)} circle: yes or no why? 3. determine if the following is a function. circle: yes or no why? (chart with x: -2, -2, 0, 0; y: -3, 3, 7, -10) 4. determine if the following is a function. (chart with x: 2, 3, 4, 5; y: 5, 5, 5, 5) circle: yes or no why?

Explanation:

1. For the set $\{(1, -1), (2, -2), (3, -3), (4, -4)\}$, each input (x-value) has exactly one unique output (y-value), so it meets the definition of a function.
2. For the set $\{(1, 3), (1, 0), (1, -2), (1, 8)\}$, the input $x=1$ is paired with multiple different y-values, violating the function definition.
3. For the given table, the inputs $x=-2$ and $x=0$ each have two different y-values, so it is not a function.
4. For the given table, every input (x-value) has exactly one output (y-value, all 5 here; repeated outputs are allowed for unique inputs), so it meets the function definition.

Answer:

1. Yes

Why? Each x has one unique y.

1. No

Why? x=1 has multiple y-values.

1. No

Why? x=-2, 0 have 2 y-values each.

1. Yes

Why? Each x has one unique y.