Functions and Function Notation

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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 is the dependent variable in a function?

Back

The dependent variable is the output of a function, which depends on the value of the independent variable.

Front

What is the independent variable in a function?

Back

The independent variable is the input of a function, which can be freely chosen.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input corresponds to exactly one output. This can be checked using the vertical line test on a graph.

Front

What does the notation f(x) represent?

Back

f(x) represents the output of the function f for a given input x.

Front

What is a mapping in the context of functions?

Back

A mapping is a visual representation of how each input is paired with an output in a function.

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function may have multiple outputs for a single input.

Front

What does it mean if f(a) = b?

Back

It means that when the input a is used in the function f, the output is b.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.