math 260 midterm notes - slope of line m=(y2-y1(x2-x1 cost function =fixed costs variable costs or a bx Price-demand function p=m-nx Revenue function

math 260 midterm notes - slope of line m=(y2-y1(x2-x1 cost...

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slope of line m=(y2-y1)/(x2-x1), cost function =fixed costs+ variable costs or a+bx, Price-demand function - p=m-nx, Revenue function r=number of items sold x price per item or xp or x(m-nx), Profit function P=R-C= x(m-nx)- (a+bx) Vertical shift y=|x|+-5, horizontal y=|x-+5|, vertical stretch/shrink y=2 or 0.5|x|, reflection y=-2|x| x=-b+- SQRT b^2-4ac / 2a quadratic x-intercept, vertex form f(x)=a(x-h)^2+k for min/max, symmetry Properties of F(x)=b^x, all pass through (0,1). All continuous, x axis is horizontal asymptote, b>1 then b^x increases as x increases, if 0<b<1, then b^x decreases as x increases, (a^z)(a^y)=a^z+y, a^x/a^y=A^x-y, (a^x)^y= a^xy y=ce^ket population growth, compound interest A=P(1+r/m)^mt m=# times per year y=log{2}x or x=2^y, properties of log functions: log{b}1=0, log{b}b=1, log{b}b^x=x, b^log{b}x= x, log{b}MN=log{b}M+log{b}N, log{b}M/N= log{b}M- log{b}N, log{b}M^p = p log{b}M, log{b}M= log{b}N (M=N)

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