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Graph the following equations.

1. 3 2

2. 2

y x

y x

Math II

UNIT QUESTION: How are absolute value equations similar to piecewise functions?Standard: MM2A1

Today’s Question:How are absolute value equations similar to piecewise functions?Standard: MM2A1.a,b

Absolute Value as Piecewise Functions

Section 2.5

Piecewise Functions

Piecewise functions are functions that can be represented by more than one equation, with each equation corresponding to a different part of the domain.

Piecewise functions do not always have to be line segments. The “pieces” could be pieces of any type of graph.

This type of function is often used to represent real-life problems like ticket prices.

Example

f (x) =

x + 1, if x < 1

2, if 1 ≤ x ≤ 3

(x-3)2 + 2, if x > 3

Absolute Value as Piecewise

We usually write an absolute value function as f (x)= x , but since absolute value is a measure of distance and distance is always positive, it also can be written as follows:

f (x) = -x, if x < 0

x, if x ≥ 0

Writing Abs. Value as Piecewise

For I x – h I ≥ 0, simplify the equation given by distributing and combining like terms.

For I x – h I < 0, substitute –(x – h) in place of I x - h I. Then, simplify.

Example

Write y = 2 Ix – 4I – 10 as a piecewise function.

For (x-4) ≥ 0

2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4)

For (x-4) < 0

2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10

= -2x – 2 (when x < 4))

Graphs of Both

y=2x-18y=-2x-2

EOCT Practice

A

EOCT Practice

C

Writing Abs. Value as Piecewise

Using a graph

Writing Abs. Value as Piecewise

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