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Page 376-378 #22-25, 61-64 22) a)(f+g)= 2x 2 +6 b) (f-g)= -4x 2 -4 c) (fg)= -3x 4 -2x 2 +5 d) (f/g)= (1-x 2 )/(3x 2 +5) 23) a)(f+g)= 3-2x b) (f-g)= 6x-3 c) (fg)= 6x-8x 2 d) (f/g)= 2x/(3-4x); x≠3/4 61) a) 3 b) 4 62) a) 12 b) 56 63) a) 18 b) 23 64) a)1 b) 5 24) a)(f+g)= √x +3; x≥0 b) (f-g)= √x +3; x≥0 c) (fg)= 3√x ; x≥0 d) (f/g)= √x/3; x≥0 25) a)(f+g)= (x+1)/(2x-4); x≠2 b) (f-g)= (1-x)/(2x-4); x≠2 c) (fg)= x/(2x-4) 2 ; x≠2 d) (f/g)= 1/x; x≠2; x≠0
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Page 393 #13-18, 45-48 13) One to one 14) Not one to one 15) Not one to one 16) One to one 17) Not one to one 18) Not one to one 45) f -1 (x)= (x+1)/3 46) f -1 (x)= 2x+1 47) f -1 (x)= 48) f -1 (x)=
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5.3: Exponential Functions
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Objectives Distinguish between linear and exponential growth Model data with exponential growth Calculate compound interest Use the natural exponential function in applications
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What is an exponential function? f(x)=Ca x a>0 C>0 a is the base C is the coefficient a is raised to the exponent first, the multiplied by C. C is also the y intercept because a 0 =1 and C*1=C
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Linear vs. exponential Exponential functions look like
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Finding exponential growth In exponential growth, the output increases by a constant factor (a). In the ordered pair (0, ?), y=C. Check this out: x0123 y13927 x0123 y5102040
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Sketching a graph Try these f(x)= 2 x f(x)= (1/4)(2 x )
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5.4: Logarithmic Functions and Models
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5.4 Objectives Evaluate the common logarithmic function Solve basic exponential and logarithmic equations Evaluate logarithms with different bases Solve general exponential and logarithmic equations
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Common logarithm log x = k if x = 10 k Properties of this include: log 10 x = x 10 logx = x
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Base a logarithm log a x = k if and only if.. x=a k a>0 and not equal to 1 k is a real number
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Properties of base a logarithms log a a x =x (for any real number x) a log a x =x (for any positive number x)
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Connecting to Inverses The inverse function of f(x)=a x Is….. log a x
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HOW TO SOLVE LOGARITHMIC EQUATIONS In the form log a x=k 1)Exponentiate each side with the base (a) to make the log side equal x. 2)Use the inverse property to find x.
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Try these log 4 16 = x
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Try these log 2 16 = x
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Solving exponential equations In the form a x =k. 1)Take log base a on both sides, to make a x equal x. 2)Use the inverse property to find x.
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Try these 4 x = 1/16
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Try these 2 x = 16
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Your assignment Page 413 – 19-23 – 43-48 Page 430 – 2-18 even – 49-68
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