Midterm_1_reference_sheet

Midterm_1_reference_sheet - 2 a f ( cx ) dilates by factor...

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Math 4C Fall 2007 Midterm 1 Reference Sheet Distance between two points Linear equations d = ( x 2 " x 1 ) 2 + ( y 2 " y 1 ) 2 General form Ax + By = C Midpoint between two points Slope-intercept form y = mx + b ( x 1 + x 2 2 , y 1 + y 2 2 ) Point-slope form y " y 1 = m ( x " x 1 ) Slope between two points m = y 2 " y 1 x 2 " x 1 Double-intercept form x a + y b = 1 Average rate of change of a function Quadratic equations " y " x = f ( x + h ) " f ( x ) h or " y " x = f ( b ) " f ( a ) b " a Forms General f ( x ) = ax 2 + bx + c Composition of two functions ( f o g )( x ) = f [ g ( x )] Vertex y = a ( x " h ) 2 + k Inverse function Factored f ( x ) = a ( x " r 1 )( x " r 2 ) f " 1 [ f ( x )] = f [ f " 1 ( x )] = x Vertex General ( " b 2 a , f ( " b 2 a )) Even function f ( " x ) = f ( x ) Vertex ( h , k ) Odd function f ( " x ) = " f ( x ) Factored ( r 1 + r 2 2 , f ( r 1 + r 2 2 )) Transformations of graph of f(x) Axis General x = " b 2 a f ( x " h ) + k translates h units "to the right", Vertex x = h k units vertically " f ( x ) reflects across x -axis; f ( " x ) across y -axis Factored x = r 1 + r 2 2 cf ( x ) dilates by factor of c vertically; Roots General x = " b ± b 2 " 4 ac
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Unformatted text preview: 2 a f ( cx ) dilates by factor of 1 c horizontally Vertex x = h k a Factored x = r 1 , x = r 2 Logarithms Definition of logarithm log b x = y is equivalent to b y = x Properties of logarithms log b b = 1 log b 1 = ( b , P and Q are positive, b &quot; 1 ) log b PQ = log b P + log b Q log b ( P Q ) = log b P &quot; log b Q log b P n = n log b P b log b P = P Change of base formula log a x = log b x log b a Exponential growth and decay Compound interest (period) A = P (1 + r n ) nt Compound interest (continuous) A = Pe rt Exponential growth/decay formula N t ( ) = N e kt , (growth), N t ( ) = N e &quot; kt (decay)...
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