Unit 1: Non-Trig Functions PSHS Precalculus Parent Functions, Transformations & Piecewise Functions Subject to change

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1 Unit : Non-Trig Functions PSHS Precalculus Parent Functions, Transformations & Piecewise Functions Subject to change Monda Tuesda Wednesda Thursda Frida September Graphs and Attributes of Graphs and Attributes of =,,,, =b, logb,,,[[]] HW 6 HW End Behavior in Limit Notation Even/Odd Smmetr Card Sort Generic Transformations Discretionar Da HW 8 HW 9 HW 0 HW October 6 pep rall Shift, Stretch, Flip both Shift, Stretch, Flip both Absolute Value as a Writing Equations Horiz. and Vert. Horiz. and Vert. Transformation Transformations of Transformations of =,,,, =b, logb,,,[[]] HW HW HW HW HW Student Teacher Holida Parent/Teacher Conference Da PSAT Absolute Value as a Piecewise Function HW 7 Piecewise Functions Evaluate, Graph and Write Discretionar Da (ALEKS) end of grade period Discretionar Da HW: Review Packet Review PARENT FUNCTIONS & TRANSFORMATIONS TEST HW 6: Stud the Parent Functions completed in class toda then complete lines - on our Parent Functions Attribute Chart (eclude end behavior/limit and odd/even columns). Additionall, ou ma wish to make flashcards for each function. HW 7: Stud the Parent Functions completed in class toda then complete lines 6-0 on our Parent Functions Attribute Chart (eclude end behavior/limit and odd/even columns). Additionall, ou ma wish to make flashcards for each function. HW 8: Complete the End Behavior/Limit column on our Parent Functions Attribute Chart and tet p.: #,,, 6 (write end behavior in limit notation for each graph) HW 9: Complete the Even/Odd column on our Parent Functions Attribute Chart And algebraicall determine whether each function below has even, odd or neither tpe of smmetr. ) f ( ) ) ( ) f 6 ) f ( ) ) f ( ) ) f ( ) 6) f ( ) ( ) State the smmetr seen in each graph: 7) 8) 9)

2 HW 0: Complete Parent Functions Checklist below and make flash cards (if ou haven t alread) b transferring each of the functions to a notecard or piece of construction paper. The graph should be sketched on the front and the equation, tpe, domain, range, end behavior, zeros, smmetr and asmptotes should be written on the back. Check all that appl. Domain: Range: Range: 0, Even function Odd function No smmetr Zero at -intercept: No asmptotes Horiz. asmptote at

3 HW : Graph. ) f() ) f ) f(( + )) ) f( ) ) f ( ) 6) f ( ) f() HW : State the parent function, describe the transformations in a correct order, show the table of values, graph the transformed function and state the domain and range. ) ( ) PF: Trans: ) PF: Trans: D: R: D: R: ) ( ) PF: Trans: ) PF: Trans: D: R: D: R:

4 HW : State the parent function, describe the transformations in a correct order, show the table of values, graph the transformed function and state the domain and range. ) PF: Trans: ) PF: Trans: D: R: D: R: ) = log ( ) PF: Trans: ) = ( + ) PF: Trans: D: R: D: R: ) e PF: Trans: 6) ln( ) PF: Trans: D: R: D: R:

5 HW :. Given the graph for g() below, For problems -, Identif the parent function (PF) and transformations, in sketch the graph of g () order, make the table and draw the graph. g(). = PF:. PF: Trans: Trans: PF:. log PF: Trans: Trans: HW : Write the equation of each function after the given transformations.. Horizontall stretched b a factor of, translated units left and units down.. reflected over the -ais, verticall stretched b a factor of, and translated unit left and 6 units up base (0, 7/) Homework continues on net page!

6 HW 6: ) Graph and give domain & range: 0 ) Graph and give domain & range: f ( ) ) Graph, give domain and range, then evaluate a-d given g( ) [ ] a) g() b) g() Write the equations for the piecewise functions below: c) g(0.) d) g(-) ) ) HW 7: Write these absolute value functions as piece functions: ) f ( ) ) f ( ) ) f ( ) ) h ( ) Write an absolute value function and piecewise function for each graph: ) 6) 7) b. c.

7 ANSWERS HW 6-8 f( ) f ( ) f ( ) f ( ) f( ) Equation Graph Table of Values f( ) b, b > f( ) log, b > f( ), 0 f( ), 0 f ( ) b /b b - b /b Tpe Linear Quadratic Cubic Absolute Value Square Root Eponential Logarithmic Reciprocal Reciprocal Square Greatest Integer Domain: Range: D: (-, ) R: (-, ) D: (-, ) R: [0, ) D: (-, ) R: (-, ) D: (-, ) R: [0, ) D: [0, ) R: [0, ) D: (-, ) R: (0, ) D: (0, ) R: (-, ) D: (-,0) U (0, ) R: (-,0) U (0, ) D: (-,0) U (0, ) R: (0, ) D: (-, ) R: Integers End Behavior/ Odd/Even Zeroes Asmptotes Limit lim Odd (0,0) None lim lim lim lim lim Even (0,0) None Odd (0,0) None lim Even (0,0) None lim 0 0 lim Neither (0,0) None lim b 0 lim b lim 0 log b Neither None = 0 lim log Neither (,0) = 0 b lim 0 lim 0 lim 0 lim 0 lim Odd Even None None = 0 & = 0 = 0 & = 0 lim Neither Infinite None

8 HW 8 p. ) lim f ( ) lim f ( ) ) lim f ( ) 0 lim f ( ) 0 ) lim f ( ) lim f ( ) 6) lim f ( ) lim f ( ) HW 9: ) Neither ) Even ) Neither ) Neither ) Even 6) Neither 7) Even 8) Odd 9) Neither HW ) ) ) ) ) 6)

9 HW 0: Domain: Range: Range: 0, Even function Odd function No smmetr Zero at -intercept: No asmptotes Horiz. asmptote at

10 HW : HW ) PF Reflect over the -ais, vertical stretch of, up Reflect over -ais Domain: all reals Range: odd integers ) PF Vertical stretch of Left Domain: all reals Range: > 0 ) PF Reflect over -ais, right Domain: Range: < 0 ) PF log Vertical stretch of Domain: > 0 Range: all reals ) PF e Reflect over -ais Horizontal stretch of Domain: all reals Range: > 0 6) PF ln Reflect over -ais Vertical compress of ½ Up Domain: > 0 Range: all reals

11 HW ) ) PF down Abs.val of ) PF Right Down Abs.val of ) PF Down Abs.val of ) log PF log down abs.val of HW ( ) ) ( ) ( f ) ) ( ) 6 f ) ) ( 8) ( ) ) 6) 6 7) 8)

12 HWK 6 ) ) ) a) b) c) - d) Domain: (-, -) [0, ) Domain: (-, 0) (0, ) Range: (-, -) [0, ] Range: (0, ) ), f ( ) ),, 0 f ( ) Domain: (-, 0- (, ) log, 0 Range: [-] U [-] U [0] U [, ) HW 7,, ) f ( ) ) g ( ),, ), 0 ( ) ), 0, h ( ), or a) f ( ) or, 0 f ( ) b) f ( ) or, 0, f ( ) 7, c) f ( ) or, f ( ), or