Relations and Functions

A set of ordered pairs is called what?

{(0, 1), (1, 2),(3, 4)}

• the domain

• a relation

• a function

• the range

Answer explanation

A set of ordered pairs, like {(0, 1), (1, 2), (3, 4)}, is called a relation. It represents a relationship between elements of two sets, where each pair consists of an input and an output.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What is the domain of a relation?

• the set of all x-values

• the set of all y-values

Answer explanation

The domain of a relation refers to the set of all x-values. This means it includes every input value that can be paired with a corresponding y-value in the relation.

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

Which is the set of all y-values or outputs?

• domain

• range

• relation

• function

Answer explanation

The set of all y-values or outputs of a function is called the range. The domain refers to the set of x-values or inputs, while a relation describes the relationship between inputs and outputs.

Tags

CCSS.HSF.IF.A.1

What is the range of the mapping?

• {1, 2, 4}

• {0, 1, 2, 3}

• {0, 3}

• {1, 4}

Answer explanation

The range of a mapping includes all possible output values. In this case, the correct range is {1, 2, 4}, as these are the only values produced by the mapping, while the other options include values not in the mapping.

Tags

CCSS.8.F.A.1

CCSS.8.F.B.5

Which relation does the mapping show?

• {(0, 1), (1, 2),(3, 4)}

• {(1, 0), (2, 1), (2, 2), (4, 3)}

• {(0, 1), (1, 2), (2, 2), (3, 4)}

• {(1, 0), (2, 1), (4, 3)}

Tags

CCSS.8.F.A.1

CCSS.8.F.B.4

CCSS.8.F.B.5

Which relation has a domain of {2, 6, 8}?

• {(2, 0), (4, 8), (6, 2), (8, 0)}

• {(6, 1), (6, 2), (2, 4), (8, 6)}

• {(1, 8), (2, 2), (2, 6)}

• {(8, 6), (2, 8), (8, 2)}

Answer explanation

The relation {(6, 1), (6, 2), (2, 4), (8, 6)} has a domain of {2, 6, 8} because it includes the first elements 2, 6, and 8. The other options include elements outside this set.

Identify each relation that represents a function.

• {(1, -4), (2, 3), (4, 1), (5, 2)}

• {(4, 6), (2, 6), (-1, 6), (3, 6)}

• {(3, 7), (4, 9), (3, 3), (5, -1)}

• {(-3, 7), (4, 9), (-3, -3), (5, -1)}

Answer explanation

A function must have unique outputs for each input. The first choice has unique outputs, and the second choice has the same output for different inputs, which is acceptable. The other choices have repeated inputs, thus not functions.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What is the range of the relation?

• {-2, 1, 3}

• {-2, 1, 2, 4}

• {y | -2 ≤ y ≤ 2}

• {y | -4 ≤ y ≤ 4}

Answer explanation

The range of a relation consists of the output values. The correct choice {-2, 1, 3} includes all unique output values, while the other options either include extra values or represent ranges that do not match the outputs.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

• {-6, -5}

• {-6, -5, -4}

• {-5, -4, -3}

• {-5, -4}

Answer explanation

To find the range of y = x^2 - 5 for the domain {-1, 0, 1}, calculate y for each x: y(-1) = -4, y(0) = -5, y(1) = -4. The outputs are {-4, -5}, so the range is {-5, -4}, which matches the correct answer.

Tags

CCSS.HSA.SSE.A.1

Which graph apparently represents a function of x?

• 
• 
• 
• 

Answer explanation

This graph passes the vertical line test.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.5

CCSS.HSF.IF.C.7