Lines and Operations
Popular in Analytic Geometry/Calculus I
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This 3 page Class Notes was uploaded by Deryn Susman on Friday September 30, 2016. The Class Notes belongs to MA121-02 at Wagner College taught by Florin Pop in Fall 2016. Since its upload, it has received 6 views. For similar materials see Analytic Geometry/Calculus I in Math at Wagner College.
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Date Created: 09/30/16
Lines and Operations 9/7/2016 By Deryn Susman Lines “Rise over run” is a constant called slope (“m”). The slope of the line passes through 2 points. m = (y2−y 1/(x 2x )b A point and a slope determine one line. Slope-InterceptForm y = mx+b Horizontallines havem=0 y=b Verticallines havem=undefined x=constant Operations with Functions Addition: If f and g are functions, the sum of f+g is a rule which operates as follows (f+g)(x)=f(x)+g(x) X mustbe in the domain off and g. Thenew domain consists of inputs common tofand g. Domain ⊘= no x, no solution, empty set, no domain Other operations: f(x)-g(x) f(x)/g(x) f(x)g(x) Compositions of Functions Decompose Write 1/(x+5) as f ° (“f of g”) “How do I get from x to 1/(x+5) in steps Even and Odd Functions A function f(x) is called “even” if f(-x) = f(x) x , x , x eve, |x|, cosx Examples: Graphically, everything on the positive side is mirrored by negative side. A function f(x) is called “odd” if f(-x) = -f(x) 3 odd Examples: x, x , x , sinx, tanx The graph reflects over the origin. 2 **There are functions that are neither even nor odd. Ex. f(x)= x+x
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