Math Final Cheat Sheet.docx - Big Graphs Rate of change the...

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Big Graphs Rate of change- the amount y changes as x changes Global=Absolute, Local=Relative If + or - ∞ is the highest or lowest point, there is no max or min Concavity- the rate of change of a function. If a function is linear, it has no concavity. Rules - if there is discontinuity, be careful about notation (bracket or parentheses) for domain and range. If it is a segment, it cannot be a local max or min. But if the hole is filled in, it could POSSIBLY be a global max. Functions Composition: Notation : f(g(x)) or (fog)(x) or fog:x Ex : f(x)= x 2 g(x)= x+2 f(g(2))= (x+2) 2 Deconstructing : Ex : h(x)= + 7 -In g(x)= -Out f(x)= x+7 The parent graph of a rational (aka reciprocal) function is f(x)= 1/x Vertical asymptotes can never be crossed, while horizontal asymptotes may be. How to find VA- 1.) factor both the numerator and the denominator, cancel if possible. 2.) if a factor doesn’t cancel in the denom, then there is a va at x=a . 3.) If a factor doesn’t cancel, then there is a hole. How to find HA - 1.) Look at the leading term of both the numerator and the denom. 2.) If the degree of the denom is higher, then y=0 is the HA. 3.) If the degrees are equal, HA is at y=c ,
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