Understanding Functions through Ordered Pairs

The video tutorial explains how to determine if sets of ordered pairs represent valid functions. It reviews the definition of a function, emphasizing that each input must have exactly one output. The tutorial analyzes four sets of ordered pairs, identifying which are functions and which are not, based on whether inputs have unique outputs. The video also demonstrates mapping functions and relations to visualize the input-output relationships.

What is a key characteristic of a function in terms of inputs and outputs?

• Each input can have multiple outputs.

• Each input has exactly one output.

• Each output can have multiple inputs.

• Each output has exactly one input.

In the first set of ordered pairs, what is the range?

• {negative four, three, five, eight, and 15}

• {negative three, two, four, seven, and 14}

• {negative four, negative three, negative two, negative one, and zero}

• {negative two, two, four, seven, and sixteen}

Why is the second set of ordered pairs not a function?

• It has repeated outputs for the same input.

• It has multiple inputs for the same output.

• It has no outputs for some inputs.

• It has the same input with different outputs.

What is the domain of the second set of ordered pairs?

• {negative four, three, five, eight, and 15}

• {negative four, negative three, negative two, negative one, and zero}

• {negative two, two, four, seven, and sixteen}

• {negative one, positive one, nine, and ten}

In the third set of ordered pairs, what is the issue with the input values?

• Inputs are not numbers.

• All inputs are the same.

• All inputs are different.

• Inputs are missing.

What is the range of the third set of ordered pairs?

• {negative four, three, five, eight, and 15}

• {negative one, positive one, nine, and ten}

• {negative four, negative three, negative two, negative one, and zero}

• {negative two, two, four, seven, and sixteen}

Why is the fourth set of ordered pairs considered a function?

• Each output has exactly one input.

• Each output has multiple inputs.

• Each input has exactly one output.

• Each input has multiple outputs.

What is the domain of the fourth set of ordered pairs?

• {negative two, two, four, seven, and sixteen}

• {negative one, positive one, nine, and ten}

• {negative four, three, five, eight, and 15}

• {negative four, negative three, negative two, negative one, and zero}

What is the range of the fourth set of ordered pairs?

• {negative four, negative three, negative two, negative one, and zero}

• {five}

• {negative four, three, five, eight, and 15}

• {negative one, positive one, nine, and ten}

In the context of functions, what does the term 'domain' refer to?

• The set of all possible outputs.

• The set of all possible inputs.

• The set of all possible ordered pairs.

• The set of all possible functions.