FIRE UP! With your neighbor, simplify the following expression and be ready to share out ! Ready GO! (x + 3) 2 WEDNESDAY

Graphing Parent Functions and Functional Notation Chapter 1 Section 1-2,3,5

Objectives I can sketch parent function graphs using critical points I can find functional values of any function –From an equation –From a graph

Functions A function is a special relation in which each element from the domain is paired with exactly one element from the range.

Function A function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range. FunctionNot a Function  749  

SOLUTION GUIDED PRACTICE for Example 2 Tell whether the pairing is a function Output Input The pairing is a function because each input is paired with exactly one output.

Parent Functions These are the 8 parent functions for this unit!! –Constant –Linear –Quadratic –Cubic –Absolute Value –Square Root –Reciprocal –Greatest Integer

Critical Points You must graph all the critical points for each function! 10x10 Grid all year

Graph: f(x) = 0

Linear What are critical points Xy

Graph: f(x) = x

Quadratic What are critical points Xy

Graph: f(x) = x 2

Graph: f(x) =

Square Root What are critical points Xy

Graph: f(x) =

Functional Notation Functional notation is a way to express an equation as a function If we have an equation y = 2x + 3 We can write this in functional notation as: f(x) = 2x + 3 f(x) replaces the y It is read “f of x” x is the input and f(x) is the output

Finding a Functional value f(x) = 6x + 10 Find f(-3) This means substitute –3 for all x variables and evaluate f(-3) = 6(-3) + 10 = = -8 g(x) = 2x 2 + 4x – 1 Find g(-3) g(-3) = 2(-3) 2 + 4(-3) – 1 2(9) + (– 12) – 1 18 – 12 – 1 5

What does this mean? f(3) This reads as “ f of 3” Simply put: “What is the y-value for an x-input of 3

SOLUTION EXAMPLE 5 Evaluate functions Evaluate the function when x = – 4. a. f (x) = – x 2 – 2x + 7 Write function. f (– 4) = –(– 4) 2 – 2(– 4) + 7 Substitute –4 for x. = –1= –1 Simplify.

Practice Problem Given f(x) = x 2 + 2x – 1, find f(2). Practice Problem Given f(x) = x 2 + 2x – 1, find f(–3). f(2) = (2) 2 +2(2) – 1 = – 1 = 7 f(–3) = (–3) 2 +2(–3) – 1 = 9 – 6 – 1 = 2 Evaluate Given f(x) = x 2 + 2x – 1 = 2 + – – 1. Given that f(x) = 3x 2 + 2x, find f(h). f(h) = 3(h) 2 + 2(h) = 3h 2 + 2h

From a Graph You can also pick functional values from a graph Remember f(x) replaced “y” So, you are just finding y-values corresponding to the x-values

Step It Up Find f(x + 2)

Homework WS 1-2 Signed Paperwork and Supplies if you forgot Work on Parent Function Packets