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Algebra 2 H Week 3 September 8-11Topics: Piecewise-Defined Functions, Function Composition and Operations, & Inverse Functions Test 1: Wednesday 9/9

+4-1: Piecewise Functions (SB pg. 57-60)Objectives: Graph piecewise-defined functions & write domain/range of functions in interval notation, inequalities and set notation.

A piecewise-defined function is a function that is defined using different rules for the different nonoverlapping intervals of its domain.

+ Domain: set of input values (x-values)Range: set of output values (y-values) Example:

Domain: Range:

+ Domain: set of input values (x-values)Range: set of output values (y-values) Example:

Domain: ( -∞,∞)

[-3,∞)Range:

+Notations

Domain: ( -∞,∞)

[-3,∞)Range: 1. Interval Notation

2. Set NotationDomain: {x | x ∈

R} Range: {y| y ∈ R, y ≥ -3}

3. Inequality NotationDomain: Range: -∞< x

<∞ y ≥-3

+ Find the domain and range of the following piecewise

functionsA.

+ Find the domain and range of the following piecewise

functionsB.

+ Find the domain and range of the following piecewise

functionsC.

+Graphing Functions

+ 4-2: Step Functions SB pg. 61-64

A step function is a piecewise-defined function whose value remains constant throughout each interval of its domain.

𝑓ሺ𝑥ሻ= ቐ −2 𝑖𝑓 𝑥< −31 𝑖𝑓− 3 ≤ 𝑥< 23 𝑖𝑓 𝑥≥ 2

SB pg. 61 Q1

Domain:Range:

+4-2 Absolute Value Functions

𝑓ሺ𝑥ሻ= ቄ− 𝑥 if  𝑥< 0 𝑥 if  𝑥≥ 0

Domain:Range:

Does the function have a minimum or maximum value?

X-intercept(s):Y-intercept(s):Describe the symmetry:

𝑔 (𝑥 )=|𝑥|or

+ Absolute Value Transformationsy = -a |x – h| + k

* Note: (h, k) is your vertex*

Reflection across the

x-axisVertical Stretch

a > 1(makes it narrower)

ORVertical

Compression 0 < a < 1

(makes it wider)

Horizontal Translation

(opposite of h)

Vertical Translation