Warm Up Graph the following on an x,y axis using the table method y = -2x + 6 Graph the following on a number line X > 5 and X ≤ -1

How do we graph piecewise functions? Math II Day 42 (10-11-10) Standard MM2A1.b Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and end behavior. Today’s Question: How do we graph piecewise functions?

2.5 Piecewise Functions

f(x) = 5x+3 when x > -1 Domain : [-1, +∞] Range : [ -2, +∞]

When they give you an X …you must choose it f(x) = 2x+4 x≥-3 x 2x+4 y (x,y) -3 2(-3)+4 -2 (-3,-2) 1 2(1)+4 6 (1,6) Domain : [-3, +∞] Range : [ -2, +∞]

When they give you an X …you must choose it f(x) = -2x+1 -2<x<4 x -2x+1 y (x,y) -2 -2(-2)+1 5 (-2,5) 4 -2(4)+1 -7 (5,-7) Domain : [-2, 4] Range : [ -7, 5]

Graphing Work Sheet Fill out the table Graph each function Give the domain and range

Up to now, we’ve been looking at functions represented by a single equation. In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. These are called piecewise functions.

Evaluate for the following X = - 4 X = 3 X = 1 2(-4) – 1 = -9 3(3) + 1 = 10 2(1) – 1 = 1

Evaluate f(x) when x=0, x=2, x=4 First you have to figure out which equation to use You NEVER use both X=4 X=2 X=0 This one fits Into the top equation So: 0+2=2 f(0)=2 So: 2(4) + 1 = 9 f(4) = 9 This one fits here So: 2(2) + 1 = 5 f(2) = 5 This one fits here

EVALUATE PROBLEMS Evaluate for x = 5, 4, -8, 10, 0, 2, -4

Evaluate Worksheet Evaluate each problem for the numbers given