College Algebra K/DC Monday, 25 January 2016 OBJECTIVE TSW graph basic functions. TODAY’S ASSIGNMENT –Sec. 2.6: pp (1-10 all, all) –WS Greatest Integer Function QUIZ: Sec. 2.4 – 2.5 has been moved to tomorrow, Tuesday, 26 January BATTERIES OR BATTERY MONEY ! ! !

2-2 Graphs of Basic Functions 2.6 Continuity ▪ The Identity, Squaring, and Cubing Functions ▪ The Square Root and Cube Root Functions ▪ The Absolute Value Function ▪ Greatest Integer Function

Continuity (Informal Definition) A function is continuous over an interval of its domain (x-values) if its hand-drawn graph over that interval can be sketched without lifting the pencil from the paper. In this unit, you should be able to provide a quick, rough, accurate sketch of the parent functions and their domains and ranges without a calculator! –Part of the test (Friday, 29 January 2016) will be without calculator.

2-4 Describe the intervals of continuity (IOC) for each function. Determining Intervals of Continuity

You should be able to graph these parent functions without a calculator and identify their domains and ranges. 1.Identity Function: Domain: (–∞, ∞)Range: (–∞, ∞) 2.Square Function: Domain: (–∞, ∞)Range: [0, ∞) 3.Cubic Function: Domain: (–∞, ∞)Range: (–∞, ∞) 4.Square Root Function: Domain: [0, ∞)Range: [0, ∞) 5.Cube Root Function: Domain: (–∞, ∞)Range: (–∞, ∞) 6.Absolute Value Function: Domain: (–∞, ∞)Range: [0, ∞)

Greatest Integer Function The greatest integer function is the greatest integer less than or equal to the argument. The argument is the value inside the double brackets. Sometimes it is x, sometimes it is an expression with x. It is also referred to as a step function. The best method to graph the greatest integer function is to make a table of x-values.

Greatest Integer Function The greatest integer function is the greatest integer less than or equal to the argument. Ex: –1–2–3–4–5–6

x 1 / 3 x – Graphing a Greatest Integer Function Graph Create a table of sample ordered pairs: –1–2–3–4–5–6 –4 –5 –11/3  –3.67 –4 –3 –2 –10/3  –3.33 –8/3  –2.67 –4 –3

2-9 Graphing a Greatest Integer Function Graph

Assignment Sec. 2.6: pp (1-10 all, all) –Due tomorrow, Tuesday, 26 January 2016.

College Algebra K/DC Tuesday, 26 January 2016 OBJECTIVE TSW graph piece functions. TODAY’S ASSIGNMENT (I’ll collect individually) –Sec. 2.5: p. 226 (1-8 all, all, all, all) –Sec. 2.5: pp (9-12 all, all, 25, 26, 28, all) –Sec. 2.6: pp (1-10 all, all) –WS Greatest Integer Function TODAY’S ASSIGNMENT (due on Friday, 01/29/16) –Sec. 2.6: pp (17-33 all) TEST: Sec. 2.4 – 2.6 is this Friday, 29 January QUIZ: Sec. 2.4 – 2.5 will be given after the lesson. BATTERIES OR BATTERY MONEY ! ! !

ASSIGNMENT Sec. 2.6: p (17-33 all) Due on Friday, 29 January For each piecewise-defined function, find (a) f (–5), (b) f (–1), (c) f (0), and (d) f (3). Graph each piecewise-defined function.

ASSIGNMENT Sec. 2.6: p (17-33 all) Due on Friday, 29 January Graph each piecewise-defined function.

WS Sec. 2.6: Greatest Integer Function 1)(a) 0(b) 2(c) −9(d) 6(e) −2 2)(a) 0(b) 1(c) −5(d) 3(e) −1 3)(a) 4(b) 11(c) −23(d) 22(e) −1 4)(a) −1(b) 1(c) −19(d) 11(e) −4 5)(a) 1(b) −4.6(c) 18.3(d) −11(e) 3.4

2-15 Graphs of Basic Functions 2.6 Piecewise-Defined Functions

Find each of the following: a)f (–3) b)f (4) c)f (10) = –10 = 11 = –14

2-17 Graph Graphing Piecewise-Defined Functions

2-18 Graph Graphing Piecewise-Defined Functions

2-19 Graph Graphing Piecewise-Defined Functions

ASSIGNMENT Sec. 2.6: p (17-33 all) Due on Friday, 29 January For each piecewise-defined function, find (a) f (–5), (b) f (–1), (c) f (0), and (d) f (3). Graph each piecewise-defined function.

ASSIGNMENT Sec. 2.6: p (17-33 all) Due on Friday, 29 January Graph each piecewise-defined function.