Recognize functions from graphs - Questions

Answers

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.