+
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