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grapher and check if the yis a function of x. negative Average rate of change F (x₂)-F(x) 22-2 Tests for even or odd functions Even, F(-x) = f(x) Odd, F(-x) = -f(x) 1.6 A library of Parent Function Vertex for m f(x) acx-n)² +h Naming the functions Cubic Reciprocal pantal 1.7 Square root Constant absolute and more [These examples are the new ones] Transformations of functions Vertical and horizontal shifts O vertical shift & units upward: h(x) = f(x) + C 2 Vertical shift c units downward: h(x) = f(x) -( Horizontal shift c units to the right: h(x) = f(x-c) Horizontal Shift cunits to the left: h(x) = f(x + c) 8 Combination of Functions: Composite functions Arithmetic Combinations of function • f(x) +9 (x) = (f+9) x [sum] here,"" meang it can write be write in two ways (f-g)(x) = f(x-g(x) [difference] 3) F (x) · g(x) = (fg)(x) [ Product] F(x) จ (€ ) (x) = FCM), 8<x)+ 0 [Quotient] > Composition of Two Functions gr] €€ (fog)(x) = f(g(x)) [read as "f composed with gr The domain of fog is the set of all in the domain of g such that g(x) is in the domain of f. Decomposing a Composite Function "a composite function AND 50 To decompose" a look for an inner are function and an outer function. 1.9 Inverse Functions It is a function opposite of composite Function. To find an inverse function Swith the "x" and "y" *Steps to find inverse function: - Replace FCx) with y with y - Interchange - Solve for y - Rewrite y as f-1(n) Verifying Inverse: Two function, fand g, are inverse functions if and only if: f(g(x)) = x= and g(f(x)) = One-to-one Functions: A function is one to one if each value of the dependent variable corresponds to exactly one value of the independent variable. Heaning, Both the functions have to have Horizontal Test: one output. A function F has an inverse function if and only if no horizontal line intersects the graph of f at more than one point. 110 □Least Squares Regression It is an method use to find the line of the "best fit between a dependent variable and one more independent variables Mathematical Modeling and Variation 1 To find a model that approx the data most accurately, stater statisticians use a measure called the sum of the squares differences □ Direct Variation There are 2 basic types of linear models. The pter simpler model has a y-intercept that is zero. For this, "y" is said to vary as x, or to be directly proportional to n y=kx - Hore infos: - y varies directly as n - y is directly proportional tox y=kx for some non-zero constant k "k" is the constant of variation or the constant of proportionality. directly □ Direct Variation as an nth Power. - y varies directly as the nth power of y is directly proportional to the nth power of * y= K₂ for some constant k y=kxn □ Inverse Variation The following statements are equivalent: y varies inversely as x y is inversely proportional to - y = for some constant k - 1 □ Joint Variation -Z varies jointly as x and y Z is jointly proportional to mandy z=kny for some constant ts. If x,y, and z are related z=kxym by an equation of the form the z varies jointly as the nth power of* and the ith power of y.