Evaluating Functions

1. The table compares the number of songs and the number of videos Ruby's friends keep on their mobile phones.

Can the number of videos Ruby's friends keep on their phone be represented as a function of the number of songs?

Choose 1 answer:

A. Yes

B. No

2. The table compares the shoes worn by customers in an ice cream shop and the ice cream flavor that they picked.

Can ice cream flavor be represented as a function of the type of shoe?

Choose 1 answer:

A. Yes

B. No

3. Erica chops wood in the forest.

The table compares the number of cans of insect repellent Erica uses and the number of mosquito bites she gets each day.

Can the number of mosquito bites be represented as a function of the amount of repellent used?

Choose 1 answer:

A. Yes

B. No

4. The table compares the sizes (in grams) of rice packs and their cost (in dollars) for several different convenient stores.

Can the size of a pack be represented as a function of its price?

Choose 1 answer:

A. Yes

B. No

1. B. No

We are asked whether the number of videos each of Ruby's friends keeps on his or her phone can be represented as a function of the number of songs on that friend's phone. Therefore, in this case, Songs is the independent (or domain) variable and Videos is the dependent (or range) variable.

Now we can view the table as if it describes a mapping from the domain of numbers of songs to the range of numbers of videos (see below). A mapping like this represents a function if and only if every domain value is mapped to exactly one range value.

To put it another way, if we can find a domain value that is mapped to more than one range value, then the table cannot represent a function. Based on this principle, can this table represent a function?

By inspection of the table, we can see that the domain value $125$ is mapped to both the range value $54$ and the range value $66$. In other words, if we know that a friend of Ruby has $125$ songs on his or her phone, we cannot be certain about the number of videos on that friend's phone.

No!

The number of videos each of Ruby's friends keeps on his or her phone cannot be represented as a function of the number of songs on that friend's phone.

2. B. No

We are asked whether the flavor of ice cream a client picked can be represented as a function of that client's type of shoe. Therefore, in this case, Shoe type is the independent (or domain) variable and Ice cream flavor is the dependent (or range) variable.

Now we can view the table as if it describes a mapping from the domain of shoe types to the range of ice cream flavors (see below). A mapping like this represents a function if and only if every domain value is mapped to exactly one range value.

To put it another way, if we can find a domain value that is mapped to more than one range value, then the table cannot represent a function. Based on this principle, can this table represent a function?

By inspection of the table, we can see that the domain value Sandals is mapped to both the range value Chocolate and the range value Banana. In other words, if we know a client wore sandals, we cannot be certain about the ice cream flavor that client picked.

This is the only case where a domain value is mapped to more than one range value, but even a single case is enough to determine that the table cannot represent a function.

No!

The flavor of ice cream a client picked cannot be represented as a function of that client's type of shoe.

3. A. Yes

We are asked whether the number of mosquito bites can be represented as a function of the amount of repellent used. Therefore, in this case, Cans of repellent is the independent (or domain) variable and Mosquito bites is the dependent (or range) variable.

Now we can view the table as if it describes a mapping from the domain of numbers of cans to the range of numbers of bites (see below). A mapping like this represents a function if and only if every domain value is mapped to exactly one range value.

To put it another way, if we can find a domain value that is mapped to more than one range value, then the table cannot represent a function. Based on this principle, can this table represent a function?

Let's inspect each domain value separately:

• The domain value $4$ appears twice in the table, but both times it's mapped to the range value $5$.
• The domain value $2$ appears twice in the table, but both times it's mapped to the range value $9$.
• The other domain values appear only once, so of course they are each mapped to only one range value.

So every domain value is mapped to exactly one range value. In other words, if we know the number of cans of repellent Erica used on a given day, we can be certain about the number of mosquito bites she got that day. Therefore, the table can indeed represent a function.

Yes!

The number of mosquito bites can be represented as a function of the amount of repellent used.

4. B. No

We are asked whether the size of a pack can be represented as a function of its price. Therefore, in this case, Price of a pack is the independent (or domain) variable and Size of a pack is the dependent (or range) variable.

Now we can view the table as if it describes a mapping from the domain of prices to the range of rice amounts (see below). A mapping like this represents a function if and only if every domain value is mapped to exactly one range value.

To put it another way, if we can find a domain value that is mapped to more than one range value, then the table cannot represent a function. Based on this principle, can this table represent a function?

By inspection of the table, we can see that the domain value $1.90$ is mapped to both the range $850$ and the range value $950$. In other words, if we know that the price of a pack is $$1.90$, we cannot be certain about the size of that pack.

This is the only case where a domain value is mapped to more than one range value, but even a single case is enough to determine that the table cannot represent a function.

No!

The size of a pack cannot be represented as a function of its price.

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.