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Admission in India 2015 By: admission.edhole.com
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Transcript of admission in india 2014

  • 1. Admission in India 2015By:admission.edhole.com

2. Essential Questions1)What is the differencebetween an odd and evenfunction?2)How do you performtransformations onpolynomial functions?admission.edhole.com 3. Even and Odd Functions(graphically)If the graph of a function is symmetric withrespect to the y-axis, then its even.If the graph of a function is symmetric withrespect to the origin, then its odd.admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 3 4. Even and Odd Functions(algebraically)A function is even if f(-x) = f(x)If you plug in -x and get the original function,then its even.A function is odd if f(-x) = -f(x)If you plug in -x and get the opposite function,then its odd.admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 4 5. Lets simplify it a little We are going to plug in a number tosimplify things. We will usually use 1and -1 to compare, but there is anexception to the rule.we will seesoon!admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 5 6. Even, Odd or Neither? f (x) = x Ex. 1Graphically Algebraicallyf (x) = xf (1) = 1 =1f (-1) = -1 =1They are the same, so it is.....admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 6 7. f (x) = x3 - xEx. 2Even, Odd or Neither?Graphically AlgebraicallyWhat happensif we plug in 1?f (x) = x3 - xf (2) = (2)3 - (2) == 6f (-2) = (-2)3 - (-2)= -6They are opposite,soadmission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 7 8. Ex. 3Even, Odd or Neither? f (x) = x2 +1Graphically Algebraicallyf (x) = x2 +1f (1) = (1)2 +1= 2f (-1) = (-1)2 +1= 2They are the same, so.....admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 8 9. Ex. 4f (x) = x3 -1 Even, Odd or Neither?Graphically Algebraicallyf (x) = x3 -1f (1) = (1)3 -1= 0= -2f (-1) = (-1)3 -1They are not = or opposite, so...admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 9 10. Lets go to the Task.admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 10 11. WWhhaatt hhaappppeennss wwhheennwwee cchhaannggee tthheeeeqquuaattiioonnss ooff tthheesseeppaarreenntt ffuunnccttiioonnss??admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 11 12. f (x) = (x + 9)2 -14f (x) = (x + 2) - 3Left 9 , Down 14Left 2 , Down 3admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 12 13. What did the negative on the outsidedo?-f(x)Study tip: If the sign is on the outside ithas x-scapedWhat do you think the negative on theinside will do?f(-x)Reflection in the x-axisReflection in the y-axisStudy tip: If the sign is on the inside, sayy am I in here?admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 13 14. Write the Equation to this Graphy = (x - 3)2 + 2admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 14 15. Write the Equation to this Graphy = (x + 2)3 -1admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 15 16. Write the Equation to this Graphy = - x -1 +1admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 16 17. Write the Equation to this Graphf (x) = (-x)3 + 2 or f (x) = -(x)3 + 2admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 17 18. Example: Sketch the graph of f (x) = (x + 2)4 .This is a shift of the graph of y = x 4 two units to the left.This, in turn, is the reflection of the graph of y = x 4 in the x-axis.xyy = x4f (x) = (x + 2)4 y = x4admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 18 19. Compare:( ) 3 ( ) 4 3 ( ) 1 3f x = x and g x = x and h x = x4admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 19 20. Comparef (x) = x2 to f (x) = 3x2 What does the ado?Vertical stretchCompare f ( x ) = x 2 to f ( x ) = 1 x22 What does the a do?Vertical shrinkadmission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 20 21. Nonrigid Transformationsh(x) = c f(x) c >1Vertical stretchCloser to y-axis0 < c < 1Vertical shrinkCloser to x-axisadmission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 21 22. Polynomial functions of the form f (x) = x n, n 1 are calledpower functions.f (x) = x5 f (x) = x4f (x) = x2xyIf n is even, their graphsresemble the graph off (x) = x2.f (x) = x3xyIf n is odd, their graphsresemble the graph off (x) = x3.admission.edhole.comCopyright by Houghton Mifflin Company, Inc. All rights reserved. 22