Page #22-25, ) 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

Page 393 #13-18, ) 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)=

5.3: Exponential Functions

Objectives Distinguish between linear and exponential growth Model data with exponential growth Calculate compound interest Use the natural exponential function in applications

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

Linear vs. exponential Exponential functions look like

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 y

Sketching a graph Try these f(x)= 2 x f(x)= (1/4)(2 x )

5.4: Logarithmic Functions and Models

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

Common logarithm log x = k if x = 10 k Properties of this include: log 10 x = x 10 logx = x

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

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)

Connecting to Inverses The inverse function of f(x)=a x Is….. log a x

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.

Try these log 4 16 = x

Try these log 2 16 = x

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.

Try these 4 x = 1/16

Try these 2 x = 16

Your assignment Page 413 – – Page 430 – 2-18 even – 49-68