EXIT TICKET Composite Functions

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What is a composite function?

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A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (g ∘ f)(x) = g(f(x)).

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CCSS.HSF-BF.A.1C

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How do you denote the composition of two functions f and g?

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The composition of two functions f and g is denoted as g(f(x)) or (g ∘ f)(x).

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CCSS.HSF-BF.A.1C

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Given f(x) = 4x - 3 and g(x) = x^2 - 4, how do you find g(f(x))?

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To find g(f(x)), substitute f(x) into g. First, calculate f(x) = 4x - 3, then replace x in g(x) with f(x): g(f(x)) = g(4x - 3) = (4x - 3)^2 - 4.

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CCSS.HSF-BF.A.1C

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What is the result of g(f(x)) when f(x) = 4x - 3 and g(x) = x^2 - 4?

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The result is g(f(x)) = 16x^2 - 24x + 5.

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CCSS.HSF-BF.A.1C

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What is the first step in finding the composition of two functions?

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The first step is to evaluate the inner function, which is the function that is applied first.

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CCSS.HSF-BF.A.1C

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What is the significance of the order of functions in composition?

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The order of functions in composition matters because (g ∘ f)(x) is not necessarily equal to (f ∘ g)(x). The output depends on which function is applied first.

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CCSS.HSF-BF.A.1C

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How do you simplify the expression (4x - 3)^2 - 4?

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To simplify (4x - 3)^2 - 4, first expand (4x - 3)^2 to get 16x^2 - 24x + 9, then subtract 4 to get 16x^2 - 24x + 5.

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CCSS.HSA.APR.C.4

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What is the domain of a composite function?

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The domain of a composite function g(f(x)) is the set of all x in the domain of f such that f(x) is in the domain of g.

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CCSS.HSF-BF.A.1C

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What is the range of a composite function?

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The range of a composite function g(f(x)) is the set of all possible output values of g(f(x)) as x varies over the domain of f.

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CCSS.HSF-BF.A.1B

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Can composite functions be used to model real-world situations?

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Yes, composite functions can be used to model real-world situations where one quantity depends on another, such as in physics, economics, and biology.

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CCSS.HSF-BF.A.1C