Math 3 Vocabulary Flashcard #9

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to x.

Front

How can you determine if a function has an inverse that is also a function?

Back

A function has an inverse that is also a function if it is one-to-one, meaning that it passes the horizontal line test.

Front

What does it mean for a function to be discontinuous?

Back

A function is discontinuous at a point if there is a break, jump, or hole in the graph at that point.

Front

How do you find the value of a function at a specific point, such as f(2)?

Back

To find f(2), substitute 2 into the function's equation and solve for the output.

Front

What is the horizontal distance between two points on a graph?

Back

The horizontal distance is the absolute difference between the x-coordinates of the two points.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if different inputs produce different outputs, meaning no two x-values map to the same y-value.

Front

What is the significance of the point (3, 3) in relation to the function m(x) and its inverse?

Back

The point (3, 3) indicates that if m(3) = 3, then m⁻¹(3) = 3, showing that the input and output are the same for this point.