FLASHCARD ( 3rd PERIOD) Functions Compositions and Inverses

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 is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f o g)(x) = f(g(x)).

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What is the inverse of a function?

Back

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

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How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

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What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = √x.

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What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses if their composition results in the identity function: f(g(x)) = x and g(f(x)) = x.

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What is a transformation in the context of functions?

Back

A transformation is a change made to a function that alters its graph, such as shifting, reflecting, stretching, or compressing.

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What does it mean to shift a function left or right?

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Shifting a function left or right involves adding or subtracting a value from the input x in the function's equation.

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What is the effect of a negative sign in front of a square root function?

Back

A negative sign in front of a square root function reflects the graph across the x-axis.

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How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to the constant term and add to the coefficient of the linear term.