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Function

relation and functions notes

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Section 2-1: Relations and Functions Goal: Write the domain and range of afunction in interval notation, inequalities, and set notation. ? Domain (Independent variable, InputvaIue,x)? ?- Of 4) OO't t '? x: (iI)(3)(5 ? Range (dependent variable, output value, y)? ?* oj,,l L4- 00r7J1 4i V' x: (t, I) (3,)?, ) ? Set Notation? ?TE 4 f - s c coIIeq, o ,ftM~, ? Relation? k 4 &QA "V ? Vertical Line Test? Function- L i\ ecA'l xqvf &9rn-M (c) I Cam t- Ivt t ac, Cs). - \ MOM 4\PdY\OVU- *j t it on Me. I \uI I k t yt -rwt c, Onto Function? ea (L44Ul1 or k-nfn nc DomBIt arre i__i__ YZWiclfl ecWcpwi _iIiJ ? flJMM Li. -- Continuous Relation? ?'-.-- k efrvrj l0 wt ?.+ick st t v - ? One-to-One Function? ? tflqt iii o(vlav f1.c$

transformation and compositions notes

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I?. Ei- Pre-AP Algebra 2 Day 3 Notes: Transformations and Compositions Date Transformations y=?af[?b(x?c)](+c? c H &1M s C) t ( c) o &A \ \ on j. vri (G vv I I Graph and state the transformation y = f(x) to y = f(x - 3) + 2 y = 2f(x) y = f(2x) (, ::; 91 dt L j-vcLLNc I - VI aizA. pxvawc' 10 ticw ti a 0 10 y = f(x)to y = f(4x) 9 OY7.A4'iit cWrcc1 It C, 10 y=f(x) to y= ?f(x+2) y=f(?x) y=f(x) onicrt Cftc4ioj k horl SkICkI 10~ of O-i CtWi&'\ [r1 C,-& Lmi1z H- y = f(x) - 2 _& y = 2f(3x) + 3 -7-- - V ho?i\ cecA s\'\E4' b 3 o'iziA 1;S aN C_ Yify Compositon of functions: Putting one function into another. Ex. Given f(x) and gf4piS would be f(g(x))?"f of g of x'. **When

AP inversfunction

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Review : Inverse Functions In the last example from the previous section we looked at the two functions and and saw that and as noted in that section this means that there is a nice relationship between these two functions. Let?s see just what that relationship is. Consider the following evaluations. In the first case we plugged into and got a value of -5. We then turned around and plugged into and got a value of -1, the number that we started off with. In the second case we did something similar. Here we plugged into and got a value of , we turned around and plugged this into and got a value of 2, which is again the number that we started with. Note that we really are doing some function composition here. The first case is really, and the second case is really,

Definition and Domain of Rational Functions

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Definition and Domain of Rational Functions A rational function is defined as the quotient of two polynomial functions. f(x) = P(x) / Q(x) Here are some examples of rational functions: g(x) = (x2 + 1) / (x - 1) h(x) = (2x + 1) / (x + 3) The rational functions to explored in this tutorial are of the form f(x) = (ax+b)/(cx + d) where a, b, c and d are parameters that may be changed, using sliders, to understand their effects on the properties of the graphs of rational functions defined above. Example: Find the domain of each function given below. g(x) = (x - 1) / (x - 2) h(x) = (x + 2) / x Solution

Algebra Help

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Applying the Fundamental Concepts of Algebra An understanding of the fundamental concepts of algebra and of how those fundamental concepts may be applied is necessary in many professional and most technical careers. For engineers and scientists it is an essential requirement. The fundamental concepts of algebra are described in the preceding section of this article. How these concepts may be applied to aid in the solution of various types of mathematical problems is explained here. USING REAL NUMBERS
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