Daily Check

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Daily Check. Graph the following equations. 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.

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Daily Check

Graph the following equations.

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

x + 1, if x < 1

2, if 1 ≤ x ≤ 3

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

f (x) =

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:

-x, if x < 0

x, if x ≥ 0

f (x) =

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-2

y=2x-18

Practice
• Worksheet
Homework
• Worksheet