Evaluating Functions

1. A. Yes

A graph represents a function if and only if every $x$-value on the graph corresponds to exactly one $y$-value.

To put it another way, if we can find an $x$-value with more than one corresponding $y$-value, then the graph doesn't represent a function.

Based on this principle, does this graph represent a function?

Yes! Every $x$-value has exactly one $y$-value that corresponds to it, so the graph represents a function.

2. B. No

A graph represents a function if and only if every $x$-value on the graph corresponds to exactly one $y$-value.

To put it another way, if we can find an $x$-value with more than one corresponding yyy-value, then the graph doesn't represent a function.

Based on this principle, does this graph represent a function?

No! For instance, the $x$-value $0$ corresponds to the $y$-value $4$, the $y$-value $-3$, and the $y$-value $-7$.

There are more cases where an $x$-value has more than one corresponding $y$-value, but even a single case is enough to determine that the graph doesn't represent a function.

No, the graph does not represent a function.

3. A. Yes

A graph represents a function if and only if every xxx-value on the graph corresponds to exactly one $y$-value.

To put it another way, if we can find an $x$-value with more than one corresponding yyy-value, then the graph doesn't represent a function.

Based on this principle, does this graph represent a function?

Yes! Every $x$-value has exactly one $y$-value that corresponds to it, so the graph represents a function.

4. A. Yes

A graph represents a function if and only if every $x$-value on the graph corresponds to exactly one $y$-value.

To put it another way, if we can find an $x$-value with more than one corresponding $y$-value, then the graph doesn't represent a function.

Based on this principle, does this graph represent a function?

Yes! Every $x$-value has exactly one $y$-value that corresponds to it, so the graph represents a function.