Key Features of a Function

Front

What is a function?

Back

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

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once. This is known as the Vertical Line Test.

Front

What does interval notation represent?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What do parentheses ( ) indicate in interval notation?

Back

Parentheses ( ) indicate that the endpoint is not included in the interval. For example, (a, b) means a < x < b.

Front

What do square brackets [ ] indicate in interval notation?

Back

Square brackets [ ] indicate that the endpoint is included in the interval. For example, [a, b] means a ≤ x ≤ b.

Front

What is the interval notation for the set of all x such that -9 < x ≤ -4?

Back

The interval notation is (-9, -4].

Front

What is end behavior of a function?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

What does it mean if a function's end behavior is described as 'As x → -∞, y → -∞ and As x → ∞, y → ∞'?

Back

It means that as x approaches negative infinity, y also approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity.

Front

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

Back

A one-to-one function is a function where each output is produced by exactly one input. No two different inputs can produce the same output.

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.