Functions vs. Non-Functions

Which of the following sets of ordered pairs represents a function? {(3, 2), (4, 4), (6, 3), (4, 5)}

• This set represents a function because each input has a unique output.

• This set does not represent a function because the input 4 has two different outputs.

• This set represents a function because all outputs are different.

• This set does not represent a function because it contains duplicate pairs.

What is a function?

• A function is a relation where each input (x-value) has exactly one output (y-value).

• A function is a type of equation that has multiple outputs for a single input.

• A function is a graphical representation of data points without any specific relationship.

• A function is a mathematical operation that can only be performed on integers.

What is the definition of an ordered pair?

• An ordered pair is a pair of numbers (x, y) that represents a point in a coordinate system, where x is the input and y is the output.

• An ordered pair is a single number that represents a point on a number line.

• An ordered pair is a set of two numbers that can be added together to form a sum.

• An ordered pair is a pair of letters used to denote a variable in algebra.

What is a non-function?

• A relation where each input has exactly one output.

• A relation where at least one input has more than one output.

• A function that does not follow the rules of mathematics.

• A type of equation that cannot be solved.

Does the mapping diagram with repeating input values represent a function?

• Yes, it represents a function because all inputs are unique.

• No, because there are repeating input values.

• Yes, it represents a function as long as the outputs are unique.

• No, because functions can have multiple outputs for the same input.

If a relation has the ordered pairs {(2, 3), (3, 4), (2, 5)}, is it a function?

• Yes, it is a function because each input has a unique output.

• No, it is not a function because the input 2 has two different outputs.

• Yes, it is a function because all outputs are different.

• No, it is not a function because there are no repeated inputs.

What is an example of a non-function?

• The set of ordered pairs {(1, 2), (1, 3)} because the input 1 has two outputs.

• The set of ordered pairs {(1, 2), (2, 3)} because each input has a unique output.

• The set of ordered pairs {(1, 2), (3, 4)} because there are no repeated inputs.

• The set of ordered pairs {(1, 2), (1, 2)} because the input 1 has the same output.

What is the vertical line test?

• A method to determine if a graph represents a function by checking if a vertical line intersects the graph at more than one point.

• A technique used to find the slope of a line on a graph.

• A way to measure the area under a curve in calculus.

• A test to determine if a graph is symmetrical about the y-axis.

What does it mean for a relation to be a function?

• A relation is a function if every input is paired with exactly one output.

• A relation is a function if it has at least one output for every input.

• A relation is a function if it can be represented as a graph.

• A relation is a function if it contains no repeated inputs.

Can a function have the same output for different inputs?

• No, a function cannot have the same output for different inputs.

• Yes, a function can have the same output for different inputs, as long as each input has only one output.

• Yes, a function can have multiple outputs for the same input.

• No, each input must have a unique output.