Relations and Functions

Front

What is a function?

Back

A function is a relation where each input has exactly one output.

Front

How can you determine if a relation is a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function by checking if a vertical line crosses the graph more than once.

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 the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

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 for a function to be one-to-one?

Back

A one-to-one function is a function where each output is associated with exactly one input.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form y = ax^2 + bx + c, where a ≠ 0.