Copy of Functions and Function Notation

Front

What is a function?

Back

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

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols, typically written as f(x), where f is the function name and x is the input.

Front

What does f(9) represent in function notation?

Back

f(9) represents the output of the function f when the input is 9.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Can a function have two outputs for the same input?

Back

No, a function cannot have two outputs for the same input; this would violate the definition of a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase.