Flashback #42

Front

What is a function in mathematics?

Back

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

Front

How do you determine if a relation is a function using a graph?

Back

A relation is a function if no vertical line intersects the graph at more than one point.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

What does it mean if the domain is (-∞, ∞)?

Back

It means that the function can accept all real numbers as input.

Front

What does it mean if the range is (-∞, ∞)?

Back

It means that the function can produce all real numbers as output.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

Can a function have multiple outputs for a single input?

Back

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

Front

What is a vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function by checking if any vertical line crosses the graph more than once.

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.