WARM-UP 1.Is the ordered pair (-6,-5) a solution to the inequality 2x -4y < 8? 2. Solve the linear inequalities: a.y > (3/5) x – 3 b.4x – 2y > -3

Graphing Piecewise Functions

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

Now you try! Evaluate f(x) for f(-3), f(-1), f(5)

Graph: For all x’s < 1, use the top graph (to the left of 1) For all x’s ≥ 1, use the bottom graph (to the right of 1)

x=1 is the breaking point of the graph. To graph the top equation, pick two points less than 1. Since this is a linear function we can just plot two points and connect them. To graph the bottom equation graph, pick two points greater than or equal to 1. Since this is a linear function we can just plot two points and connect them.

Now you try to Graph:

Step Functions

You try to graph :

Graphing Piecewise functions Regardless of what the piecewise function is, to graph: –Find the ‘breaking points’ and draw a dashed vertical line. –Plot points for the correct domain(s) –Determine if the graph is continuous or if it has a ‘hole’.