Question 1

Determine whether the relation is a function.
-{(-7, 7), (-7, 6), (1, -7), (5, 7), (8, 2)}

Accepted Answer

A relation is a function if each input (x-value) maps to exactly one output (y-value). In this set, the input -7 maps to two different outputs (7 and 6), so it is not a function.

Question 2

Determine whether the relation is a function.
-{(-6, 4), (-3, -9), (-1, 1), (4, -3)}

Accepted Answer

Each input (x-value) maps to exactly one output (y-value), so it is a function.

Question 3

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither.
-a is the savings account number of a customer at a bank, and b is the number of years the account has been active.

Accepted Answer

A savings account number (a) uniquely identifies a customer's account, and it does not change over time. Therefore, the number of years the account has been active (b) can be determined from the account number (a), making b a function of a. Different accounts can have the same duration of activity, but a specific account number will always lead to a specific duration, indicating that the relationship is not reversible (i.e., a is not a function of b).

Question 4

Determine whether the relation is a function.
-{(-8, 8), (-8, 9), (-1, 6), (6, -1), (8, -9)}

Accepted Answer

A relation is a function if each input (x-value) has exactly one output (y-value). In this set, the input -8 is associated with two different outputs (8 and 9), so it is not a function.

Question 5

Determine whether the relation is a function.
-{(-1, -5), (2, 1), (5, -6), (7, 3), (10, 4)}

Accepted Answer

Each input (x-value) is paired with exactly one output (y-value), so the relation is a function.

Question 6

Determine whether the relation is a function.
-{(-5, 4), (-1, 3), (1, 4), (6, -5)}

Accepted Answer

Each input (x-value) is paired with exactly one output (y-value), so the relation is a function.

Question 7

Determine whether the relation is a function.
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Accepted Answer

The answer of Determine whether the relation is a function.
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Question 8

Determine whether the relation is a function.
-{(-6, 7), (-3, -1), (3, 4), (3, -1)}

Accepted Answer

A relation is a function if each input (x-value) maps to exactly one output (y-value). Here, the input 3 maps to two different outputs (4 and -1), so it is not a function.

Question 9

Determine whether the relation is a function.
-{(-6, 1), (-3, -1), (2, 5), (2, -3)}

Accepted Answer

For a relation to be a function, each input (x-value) must correspond to exactly one output (y-value). In this set, the input 2 corresponds to two different outputs (5 and -3), so it is not a function.

Question 10

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Question 11

Determine whether the relation is a function.
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Accepted Answer

The answer of Determine whether the relation is a function.
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Question 12

Determine whether the relation is a function.
-{(3, 1), (3, 8), (4, 7), (8, -6), (11, -1)}

Accepted Answer

A relation is a function if each input (x-value) has exactly one output (y-value). Here, the input 3 is associated with two different outputs (1 and 8), so it is not a function.

Question 13

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Question 14

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Question 15

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither.
-a is the radius of any spherical bowling ball, and b is its volume.

Accepted Answer

The volume of a sphere is determined by its radius using the formula V = (4/3)πr^3, so b is a function of a. Conversely, given the volume, the radius can be determined, so a is a function of b.

Question 16

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Question 17

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Question 18

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Question 19

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither.
-a is the number of years of formal education of an adult living in the United States, and b is his or her age in years.

Accepted Answer

The number of years of formal education (a) is not uniquely determined by age (b), nor is age uniquely determined by the number of years of formal education. Therefore, neither variable is a function of the other.

Question 20

Use the vertical line test to determine whether y is a function of x.
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Accepted Answer

The answer of Use the vertical line test to determine...

Quiz 2: Functions and Graphs

Determine whether the relation is a function. -{(-7, 7) , (-7, 6) , (1, -7) , (5, 7) , (8, 2) }

Determine whether the relation is a function. -{(-6, 4) , (-3, -9) , (-1, 1) , (4, -3) }

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither. -a is the savings account number of a customer at a bank, and b is the number of years the account has been active.

Determine whether the relation is a function. -{(-8, 8) , (-8, 9) , (-1, 6) , (6, -1) , (8, -9) }

Determine whether the relation is a function. -{(-1, -5) , (2, 1) , (5, -6) , (7, 3) , (10, 4) }

Determine whether the relation is a function. -{(-5, 4) , (-1, 3) , (1, 4) , (6, -5) }

Determine whether the relation is a function. -

Determine whether the relation is a function. -{(-6, 7) , (-3, -1) , (3, 4) , (3, -1) }

Determine whether the relation is a function. -{(-6, 1) , (-3, -1) , (2, 5) , (2, -3) }

Use the vertical line test to determine whether y is a function of x. -

Determine whether the relation is a function. -

Determine whether the relation is a function. -{(3, 1) , (3, 8) , (4, 7) , (8, -6) , (11, -1) }

Use the vertical line test to determine whether y is a function of x. -

Use the vertical line test to determine whether y is a function of x. -

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither. -a is the radius of any spherical bowling ball, and b is its volume.

Use the vertical line test to determine whether y is a function of x. -

Use the vertical line test to determine whether y is a function of x. -

Use the vertical line test to determine whether y is a function of x. -

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither. -a is the number of years of formal education of an adult living in the United States, and b is his or her age in years.

Use the vertical line test to determine whether y is a function of x. -