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))

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)

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

Homework: P. 86 (3 - 6)

UNIT PROJECT DESIGNING FUNCTIONS

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)

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

missing a cubic function