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

2. + 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.

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

4. + Domain: set of input values (x-values) Range: set of output values (y-values) Example: Domain: ( -∞,∞) [-3,∞) Range:

5. + Notations Domain: ( -∞,∞) [-3,∞) Range: 1. Interval Notation 2. Set Notation Domain: {x | x ∈ R} Range: {y| y ∈ R, y ≥ -3} 3. Inequality Notation Domain: Range: -∞ < x < ∞ y ≥-3

6. + Find the domain and range of the following piecewise functions A.

7. + Find the domain and range of the following piecewise functions B.

8. + Find the domain and range of the following piecewise functions C.

9. + Graphing Functions

10. + 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.step function SB pg. 61 Q1 Domain: Range:

11. + 4-2 Absolute Value Functions Domain: Range: Does the function have a minimum or maximum value? X-intercept(s): Y-intercept(s): Describe the symmetry: or

12. + Absolute Value Transformations y = -a |x – h| + k * Note: (h, k) is your vertex* Reflection across the x-axis Vertical Stretch a > 1 (makes it narrower) OR Vertical Compression 0 < a < 1 (makes it wider) Horizontal Translation (opposite of h) Vertical Translation