Section+1.6

Sum, Difference, Product, and Quotient of Functions - we define the sum, difference, product, and quotient of f and g to be the functions whose domain are the set of all numbers common to the domains of f and g and that are defined as follows:

(f+g)(x) = f(x) + g(x) (f-g)(x) = f(g) - g(x) (fg)(x) = f(x)g(x) (f/g)(x) = f(x)/g(x), (g(x) cannot equal 0)

//**Composition of Functions by GMForward**// In Compositions of Fuctions, there is one main notation that we use. That notation is (f¤g)(x) which means "f of g of x". When you are given an f(x) function and a g(x) function is the only time you can use this notation. For example, if f(x)=3x+1 and g(x)=x² you can find (f¤g)(x) or (g¤f)(x)(f¤g)(x)interchangeably. If you're searching for you use the simple function f(x)=3x+1 and substitute everywhere there's an x for the function of g(x). So then you have (f¤g)(x)=3(x²)+1. You simplify the function by plug in in the values and you then get (f¤g)(x)=3x²+1. The answer looks simple but you have your answer to the function of (f¤g)(x). When finding(g¤f)(x), you do the same thing except you switch the functions and you're looking for "g of f of x". f(x)=2x-3;g(x)=x+1 Find f(g(x)) find g(f(x)) f(x)=2x-3 g(x)=x+1 f(g(x))=2(x+1)-3 g(f(x))=(2x-3)+1 f(g(x))=2x+2-3 g(f(x))=2x-2 f(g(x))=2x-1 You now have the answers to your functions. It’s as simple as piecing together a puzzle or fitting a circle in the circle space.

Transformations

h(x)= af(x) stretch/shrink (y values) h(x)= -f(x) flip h(x)= f(x)+h vertical shift (y values) h(x)= f(x+h) horizontal shift (x values) ALWAYS DO THE "a" TRANSFORMATION FIRST



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-- vertex form: y = a(x - h) + k
 * Transformations for Quadratics**
 * [[image:3.JPG]]
 * **Wider / Narrower; Flip if negative; Changes y values, not x**
 * [[image:2.JPG]]
 * **Move up / down**
 * [[image:1.JPG]]
 * **Move left / right; changes x values, not y**