Functions and Function Notations

Front

What is a function in mathematics?

Back

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

Front

How do you denote a function?

Back

A function is typically denoted by a letter such as f, g, or h, followed by the input in parentheses, e.g., f(x).

Front

What does f(1) mean in the context of a function?

Back

f(1) represents the output of the function f when the input x is 1.

Front

If f(x) = 2x + 1, what is f(1)?

Back

f(1) = 3.

Front

How do you find the x-value when given f(x) = k?

Back

Set the function equal to k and solve for x.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

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

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

How can you represent a function's output as an ordered pair?

Back

You can represent the output as an ordered pair (x, f(x)).

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.