Math 115 Week of Sep 28 Notes
Math 115 Week of Sep 28 Notes MATH 115
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This 5 page Class Notes was uploaded by Katlyn Burkitt on Friday October 2, 2015. The Class Notes belongs to MATH 115 at Towson University taught by Dr. David Buchoff in Summer 2015. Since its upload, it has received 29 views. For similar materials see Basic Math for the sciences in Mathematics (M) at Towson University.
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Date Created: 10/02/15
Drill September 28 quot 2015 1 What is the difference between fx c and fx c fx C Is shifted C Units vertically up fx C Is shifted C Units horizontally left Trick if a number c is outside of a function then the shift is vertical those units if a number c is inside of a function then the shift is equal to horizontal the number of units c Example Problem number 2 f x 2 There is no shift f x xix 4 The shift is horizontaly right 4 f x 2 The shift is vertically up two 3 Use the graph offx IxI to find gx Ix Note these do have a domain of negative infinity to positive infinity 4 Describe the transformation of y fx t0y fx 1 2 A horizontal shift one unit to the left A shrink factor of 13 A reflection over the xaxis Vertical shift two units down Section 26 Combinations of Functions and Composite Functions Finding Domains to functions that do not have the standard domain of 00 00 1 Rational polynomials gx 61 To find the domain of this you have to find what x cannot equal in this case x cannot equal a number that makes the denominator O x at 2 Put that domain into interval notation oo ZU Z oo 2 Square Root Functions y VX 5 To find the domain of this you have to find what values of x would make the number underneath the radical of square root symbol negative this is because you cannot take the square root of a negative number So in this case x 5 2 O thereforex 2 5 Then put it into Interval Notation 00 5 Algebra of functions The old way Add 2x 3 and x 1 2x 3 x 1 Combine like terms 3x 2 New way Given fx 2x 3 and gx x 1 find fx gx0f f gx f gx 2x 3 x 1 f gx 3x 2 Rules 1 f gx fx 906 2 f gx fx 906 3 f gx fx gx 4 x gx at 0 Composition of Functions f gx fgx Off ofg Ofx X 4gtGx 4 FgX Example Given fx 3x 4 and gx x2 2x 6find fgx Substitute gx in forx of fx fx2 2x 6 3x2 2x 6 4 fgx 3x2 6x 14 Decomposition fgx 2 Mac 2 3x2 4x 15 Break it up whats inside is one equation outside is another fx 2x5 gx3x2 4x1 Drill September 30th 2015 1 Find the domain of 5 A x219 oo 7U7oo B 1100 V9x 27x 2 3 3oo 2 Givenfx 5x 6 and gx 2x2 x 1 find fgx f2x2 x 1 52x2 x 16 fgx 10x2 5x 1 3Decompose hx xX2 5 fx x2 5906 27 Inverse Functions Determining if two functions are inverses Inverse functions undo each other If f g xAND gfx x Then they are inverses of one another Examplefx 2x gx 2 ix Inverses are written as 17 1 To determine if two given equations are inverses complete composition both ways and if the result is an x then they are inverses Example fx x 300 gx x 300 fgx x 300 300 gfx x 300 300 Solve and get only x Finding the inverse Step one Replace Replace fx withy fx 7x 5 to y 7x 5 Step two Interchange x and y x 2 7y 5 Step 3 Solve for y x 5 2 7y y Step 4 Replace y with f 1 g f 1L Inverses must pass the horizontal line test No horizontal line can intersect the graph at more than one point Yes No L V V The graph of fx and f 1xa re reflections over the line x y Ar Also the points of an inverse are opposite of each other a binfxis b ainf 1x 0r 12In fxis equal to 21inf 1x
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