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Composite Functions h(x) is a composite function when it has been created by two functions g(x) and f(x) This is different than a combined function in that the domain of the second function is restricted by the range of the first function In other words, h(x) = f(g(x))

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Order of Operations Start from the inside and work your way out MEANING: with h(x) = f(g(x)), 1. Solve for g(x) first so that you get a set of values (the range). 2. Take those values, and use it as your domain for f(x). 3. This will get you the range of h(x)

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find f g(x) [same as writing f(g(x))] f(x) = 3x - 5 g(x) = 2 - 5x - x^2 FIND f(g(2)) g(x) = 2 - 5(2) - (2)^2 g(x) = -12 f(x) = 3(-12) - 5 f(x) = - 41 Eventhough we now have one function, remember... By definition, a composite function means that the domain of f(x) is restricted by the range of g(x). What if we tried to solve in one step? Write the composite function for f g(x)......a one-step, single function

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Homework: P. 86 (3 - 6)

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UNIT PROJECT DESIGNING FUNCTIONS

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You are going to create a design using functions (desmos.com – graphing software) This project IS your test for this unit (50 points) DUE - April 14, pts - Creativity and Complexity 20 pts - used all functions and stated their domains 20 pts - A written description of every function used to create your design (include how you determined every function you created)

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CONDITIONS (at least one of each of the following) linear function quadratic function combined linear and quadratic function a cubic function that has a positive slope with two intervals of your choice for example: x ∈ (- ,-2) and (0,3) a quartic function with three x-intercepts

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missing a cubic function

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