Honors Precalc - Do Now!! Given the functions: F(x) = x g(x) = 5x + 3, Find: 1.) (f + g)(x)3.) f(g(x)) 2.) (fg)(x)4.) g(f(x)) **I will check your homework while you work. (Have out the in class packet if it was assigned as well.)

Agenda: We will be finishing Chapter 2 and reviewing this week. We will have a Chapter 2 test on Monday of next week.

Quote of the Day! “ I've missed more than 9000 shots in my career. I've lost almost 300 games. 26 times, I've been trusted to take the game winning shot and missed. I've failed over and over and over again in my life. And that is why I succeed. ” ~Michael Jordan

Example 1: Modeling Problem

Example 2: (only period 1) Find the composition of the following 3 functions f(g(h(x))) F(x) = √x G(x) = -3x - 5 H(x) = 2x + 2

Example 3: Find f(x) and g(x) so that the function can be described as y = f(g(x)) Y = √3x 2 + 2x Y = (x- 4) Y = |x - 9| Y = (x 4 - 3) 5

Example 4: Function Decomposition

Inverse Functions: What is an inverse?

One-to One: Horizontal Line Test A function that has an inverse that is also a function is one-to-one.

Inverses of Functions EXAMPLE 1: Find the inverse of the following function. sketch the function and its inverse. Check that they are in fact inverses.

Example 2: a.) Sketch the graph of b.) Find and sketch its graph.

Example 3: a.) Find the inverse of the function

Example 4: a.) Find the inverse of the function

Example 5: a.) Find the inverse of the function

Homework #8 Section 2.7 Pg. 205 #5, 6, 7, 11, 15, 25, 26, 34, 35, 39, 41, 54, 71