Functions Flashcard

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one corresponding y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

Why is the relation x = 10 and x = 40 not a function?

Back

Because it assigns two different y-values (outputs) for the same x-value (input), violating the definition of a function.

Front

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

Back

A graph is a function if every x-value has exactly one corresponding y-value, which can be verified using the vertical line test.

Front

How can you determine the speed of boats represented in a graph?

Back

By analyzing the slope of the lines representing each boat, where a steeper slope indicates a greater speed.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What is a domain in the context of functions?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is a range in the context of functions?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.