Functions and Function Notation

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

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 variable.

Front

What is the domain of a function?

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 the range of a function?

Back

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

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is a y-intercept?

Back

A y-intercept is a point where the graph of a function crosses the y-axis, meaning the input (x-value) is zero.

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if no two different ordered pairs have the same first element (x-value).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output.

Front

How do you find f(1) if f(x) = 2x + 3?

Back

To find f(1), substitute 1 for x: f(1) = 2(1) + 3 = 5.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.