Name Parent Function Library Date Sheilah Chason Math 444

Transcription

1 Name Parent Function Librar Date Sheilah Chason Math Objective: To neatl create a librar of Parent Functions that ou will refer to during this unit. Some of the functions ou are ver familiar with, some not so much. Carefull plot at least accurate points for each graph. Use rulers for straight lines. F() = f()=² F() = ³ f ( ) f( ) f( ) f ( ) ta n f ( ) sin f ( ) cos

2 f( ) f ( ) log f()=[ ] f ( ) g( ) log f () f () f ( )

3 Name Parent Function Date Sheilah Chason Math Objective: To learn how to verticall and horizontall shift functions. ) Graph f ( ) on the ais, indicating points. a) This equation can be interpreted as, The values equal the absolute values of the. b) Complete this equation, f( ) = c) Here ou are increasing the -value b. d) Graph the equation ou completed in (b), indicating points. e) How does the second graph compare to the first? ) Graph h( ) on the ais, indicating points. a) This statement can be interpreted as, b) Complete this equation, h()- = c) Graph the new function from b, indicating points. d) How does the new graph compare to h()? Summar: If = f(), then = f()+b shifts f()

4 ) Predict how the graphs of g( ) and g(-) = (-)² compare a) To better understand what happens here, fill out the chart. X G()=² G(-)=(-)² b) Graph g() and g(-) indicating points for each. c) How does g(-) compare to g()? ) Graph j ( ), indicating points. a) Complete this equation: j ( ) b) Graph the above equation, after predicting the result. c) How does j(+) compare to j()? d) How did the asmptote shift? In Summar: If = f(), then = f(+b) shifts f()

5 Name Parent Function Homework Date Sheilah Chason Math Sketch each set of graphs, indicating at least points. ) Y=F() =f()- = f()+ Y= f(+) = f(-)+ = f(+)- Indicate asmptote(s) and at least points. ) f( ) f ( ) f ( )

6 Indicate asmptote(s) and at least points. ) Graph g( ) log g( ) ) g() = / =g(-) Solve the inequalit: Prove the Identit: ) ( ) 0 sin cos csc sec

7 Name Date Sheilah Chason Parent Function Math Aim: Reflection over the -ais and ais. )Sketch f()= clearl using at least points. A) This equation can be interpreted as, The values equal the values squared. B) Complete this equation = f() = C) Here ou are negating the -values. D) Graph the equation ou completed in (B), indicating points. E) How does the second graph compare to the first? )Sketch m()=cos at each quadrantal angle. A) This equation can be interpreted as, The values are the cosine of the values. B) Complete this equation = m() = C) Here ou are negating the -values. D) Graph the equation ou completed in (B), indicating each quadrantal angle. E) How does the second graph compare to the first? Summar: If =f(), then =-f() F() is graphed below Graph f()

8 )Sketch f()= clearl using at least points. F) This equation can be interpreted as, The values equal raised to the power. G) Complete this equation f(-) = H) Here ou are negating the -values. I) Graph the equation ou completed in (B), indicating points. J) How does the second graph compare to the first? )Sketch m()=sin at each quadrantal angle. A) This equation can be interpreted as, The values are the sine of the values. B) Complete this equation m(-) = C) Here ou are negating the -values. D) Graph the equation ou completed in (B), indicating each quadrantal angle. E) How does the second graph compare to the first? Summar: If =f(), then =f(-) F() is graphed below Graph f(-) Graph f(-)

9 Etra Practice with Reflections over the -ais and -ais. )Sketch the reflection of f() = over the -ais and )Sketch the reflection of f() =,over the -ais and Write the new equation, = Write the new equation, = )If f()=, how would = - compare to f()? Sketch If f() =, how would g()= - compare to f()? Sketch g() ) If f() =, how would the graph h()= - ) Name all the parent functions that would not compare to f()? change if reflected over the -ais. 9

10 Name Parent Function Homework Date Sheilah Chason Math Sketch each set of graphs, indicating at least points. ) Y=F() =f(-) = - f() Y=- f(+) = f(-)+ =-f(-)- ) f ( ) f ( ) f () 0

11 ) Graph g() = [ ] Graph g(-)=[ - ] Graph g() = -[ ] Solve the inequalities: ) 0 ) ) Solve for, [0,0 ) cos sin 0

12 Name Parent Functions Date Sheilah Chason Math Objective: To determine how to reflect a graph over the origin and the line =. In addition, learn what odd and even functions are. When reflecting graphs ou use the same rules as when ou reflect points. You ma use the grid to plot a point and reflect accordingl to record the rules. )Recall the rules: (, ) r (, ) ais (, ) r (, ) ais (, ) r (, ) origin (, ) r (, ) Reflection over the = line. ) Graph m ( ), indicating points. a) Reflect m() over the line =, indicating points. b) What is the equation of the reflection? Summar: A reflection over the = line The two graphs will be

13 Reflecting over the Origin ) Graph f (), indicating points. a) Reflect f() over the origin, indicating points. b) What is the equation of the reflection? ) Graph f ( ), indicating points. a) Reflect f() over the origin, indicating points. b) What is the equation of the reflection? c) What other reflection of f() would have resulted in the same graph as a reflection over the origin and wh? Summar: When reflecting over the origin Reflecting over the origin is the same as which two reflections combined? F() is graphed below Sketch =-f(-) sketch =-f(-)

14 A function is said to be even if f()=f(-), In other words, if (,) is on the graph, so is (-,). This is also a reflection over Is f ( ) cos an even function? Can ou name all the parent functions that are even? A function is said to be odd if f(-)=-f() In other words, if (,) is on the graph, so is (-,-). This is also a reflection over Can ou name all the parent functions that are odd? Sketch f ( ) sin. Can ou name another function with the same Graph? -p -p/ -p -p/ p/ p p/ p p/ Practice Problems: Consider =f() as shown below. Sketch each of the following, indicating at least points.

15 ) Y = f() ) Y = f(+) ) Y = f() ) Y = f(-)- ) Y = - f() ) Y = f(-)+ Ligthl sketch the parent Function and then graph its translation on the same set of aes. It helps to move one point at a time. f ( ) Graph f ( ) f ( ) log, graph f ( ) f() = [ ], graph =f(-)

16 Name Trig Graph Shifting Date Sheilah Chason Math Shifting Trig Functions Graph one complete ccle for each: ) f()=cos(-π)+ ) g( ) sin -p -p/ -p -p/ p/ p p/ p p/ - -p -p/ -p -p/ p/ p p/ p p/ ) g( ) sin ) g( ) cos -p -p/ -p -p/ p/ p p/ p p/ - - -p -p/ -p -p/ p/ p p/ p p/ ) h( ) tan ) g( ) cos( ) -p -p/ -p -p/ p/ p p/ p p/ p -p/ -p -p/ p/ p p/ p p/ ) h( ) tan 8) h( ) sin -p -p/ -p -p/ p/ p p/ p p/ - - -p -p/ -p -p/ p/ p p/ p p/

17 Name Math Date Parent Functions Sheilah Chason Objective: To understand how to graph f( ) and f(). ) Graph f ()=³, indicating points. a) complete this equation, f() = b) Put in our own words what f() means: c) Graph = f(), indicating points. d) With our graphing calculator, graph =sin and = sin. e) What do ou notice? Summar: If = f(), then = f() is graphed b ) Complete the chart based on the graph of f() and then graph f( ) on the second set of aes. X F() F( ) Summar: If = f(), then =f( ) is graphed b Graph f() below: 7

18 Transformations with absolute value. The graph of =f() is shown. What is the equation for f()? Graph each of the following. f ( ) f ( ) f ( ) f ( ) f ( ) f ( )

19 Transformations with absolute value. The graph of =f() is shown. What is the equation for f()? Graph each of the following. f ( ) f ( ) f ( ) f ( ) f ( ) f ( )

20 Name Vertical and Horizontal Stretches and Shrinks Date Sheilah Chason Parent Function Math ) On our TI-89 graph f()=sin on [-π,π] [-,] a) Graph = f() = f() =f() (,) ( ) b) Graph = ½f() = f() =½f() (,) ( ) Summar ) On our TI-89 graph f()=sin on [-π,π] [-,] a) Graph = f() = f() =f() (,) ( ) b) Graph = f(½) = f() =f(½) (,) ( ) Summar Identif the parent function, f(), and the equation resulting from a sequence of transformations, g(). F()= f()= G()= g()= 0

21 Aim: How to graph functions with more than one horizontal transformation. Graph the following equations: 0. sin( ) cos( )

22 cos cos sin cos 0. tan tan

23 Transformation Practice Y = g() = g(+) Y = g()- = -g(-) Y = g(0.)+ g( )

24 Transformation Practice Y = g() = -g() Y = g(-)+ = g( ) Y = -g( )- g( )

25 Transformation Practice Y = g() = g(-) ( ) g = -g(+) g = g(-)

26 Y=g() =g(-) Y = g(-+)- = g(0.-) Y = -g(-) = g(-)