Function or Not a Function

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 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.

Front

What is a relation?

Back

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

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. Each input must correspond to exactly one output.

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

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where for each value of x, there is a unique value of f(x).

Front

Give an example of a relation that is not a function.

Back

An example of a relation that is not a function is the set of points {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

Front

What does it mean for a graph to be a function?

Back

For a graph to be a function, each x-coordinate must be paired with exactly one y-coordinate.

Front

What is an independent variable?

Back

An independent variable is a variable that represents the input of a function, often denoted as x.