Functions Review - Precalculus

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.

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What does it mean for a function to be continuous at a point x = a?

Back

A function is continuous at x = a if the limit of the function as x approaches a equals the function's value at a.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted as f(g(x)), is the application of g to x, followed by the application of f to the result.

Front

How do you find the limit of a function as x approaches a value?

Back

To find the limit as x approaches a value, evaluate the function at values increasingly close to that value from both sides.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^-1(x) that reverses the effect of f, such that f(f^-1(x)) = x.

Front

What is the difference between a one-to-one function and a many-to-one function?

Back

A one-to-one function has distinct outputs for distinct inputs, while a many-to-one function can have the same output for different inputs.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if any vertical line intersects the curve more than once, it is not a function.

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 is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.