CH 8: RADICALS AND INVERSES

Transcription

1 CH 8: RADICALS AND INVERSES f g: Start on the HLT: Pass if the line crosses the function, used for Finding the inverse: o Set equal to y o Switch and y o Solve for y o Put in function notation n n ) Sketch the graph of f ( ). State the domain and range. Is the inverse a function? ) Find the inverse of f ( ) ) If f ( ) 5 5, find f (). Suppose r ( ) and s( ) ) Find r s() 5) Find s ( r( )) 6) Consider the graph at the right. a. Is the graph a function? Why? b. Is the inverse a function? Why?

2 7) Solve: 88 8) Solve: ) Rationalize the denominator 8 6 0) Rationalize the denominator 8 9 ) Simplify 5 a 0 b 5 ) Simplify a 0 b ) Simplify 5 ) Simplify 5 80 y

3 CH 9: EXPONENTIAL AND LOGARITHMIC FUNCTIONS Eponential Function: y ab o b>: growth and b<: decay Eponential Form: Logarithmic Form: baseresult power o ln has base and log has base rt Continuous Interest: A Pe base power result 8 6 log log 8 6 Log Properties: logy log log y log log log y y log a Change of Base Theorem: log b a log b log a alog ) An eperiment begins with 00 bacteria. The bacteria double every hour, what will be the bacteria count in ½ hours? ) A material has a half-life of 50 years. How much of a 0 gram sample would remain after 70 years? ) Which graph could represent eponential decay? a) f ( ) b) g ( ) c) d) h ( ) () j ( ) (.) e) k( ) ln ) How much money is an account that began with $000 and earns interest at 7.75% compounded continuously after 5 years? 5) What rate would it take for an investment of $5,000 to become $,000 over a si year period if the account was compounded continuously? 6) At what interest rate compounded continuously would you have to invest your money so it would double in 6 years?

4 7) Evaluate or solve a) log, 000 b) log 0 c) log 9 d) log 5 e) log 8 f) g) log 8ln e 6 8) Solve e to the nearest hundredth. 9) Write e in logarithmic form. 0) Write log5 log as a single logarithm. ) Write log log 6 log6 as a single logarithm. ) Solve ln y ln 8 ln ) A bacteria population was counted every hour for 7 hours with the following results Hour (h) Population (p) (in hundreds) a) Fit an eponential regression model to the data. b) Use your model to estimate the population on the 0 th hour. ) Rock music has a decibel reading of 5 and other music has a decibel reading of 05. How many more times is the rock music more intense than other music? 5) Substance A has a ph level of 8 and Substance B has a ph level of 6. How many more times acidic is Substance A?

5 CH : POLYNOMIALS Difference of Squares: y y y Level of Finite Differences = Monomial/Binomial/Trinomial= Linear/Quadratic/Cubic/Quartic= ) True/False. z 6 is a trinomial. ) Give an eample of a quartic binomial. ) What are the zeros of the polynomial with equation P ( ) 5( 5) ( ) ) If ( 7) is a factor of some polynomial function P, 7 is a? 5) Write an equation for the given polynomial (scale is by ones). 6) Write an equation of a 6 th degree polynomial with zeros at: 0, /, and -5/7. 7) Factor 0 8) Factor 5 7 9) Factor 9 9 5

6 0) Factor 5y ) Factor 8 ) Factor 5 0 ) Factor ) Find the roots of 6 0 5) Find the zeros of the following polynomial: 0 5 6) Find the zeros of the polynomial. f ( ). 7) Find the product of 7 8) The data below models a polynomial function. Find the equation of the polynomial y

7 CH 0: TRIGONOMETRY SOH-CAH-TOA Law of Cosines: c a b sin A sin B sin C Law of Sines: a b c ab cos C Unit Circle: (cos,sin ) 0= sin sin80 5= sin cos90 60= sin cos ) In the triangle, find 5 ) In the triangle, find. 8 ) A ski slope is 580 meters long with a vertical drop of 50 meters. What is the angle of descent? ) An airplane makes a smooth final descent to the runway from an altitude of 5,000 feet when it is 0,000 horizontal feet away. At what angle of depression will the plane descend? 5) cos 6 o = sin 6) sin 5 o = sin 7

8 7) Convert 6 to radians 8) Convert 7 to degrees. 8 9) If sin, find cos 0) If cos, find tan ) If sin. 8, find all possible angles 0 80 ) Find the eact value using the unit circle. a) cos 90 b) sin 0 c) cos 5 d) sin 0 e) tan 70 f) cos g) 7 sin 6 h) i) j) k) l) tan 5 cos tan cos 5 tan 6 ) Find LM M ) Find m L 6 B L 9 M 8 o o 0 o N L 5) Graph y= sin a) State the period. b) Find the domain. c) Find the range. 8

9 CH : MATRICES To add/subtract matrices dimensions must To multiply matrices dimensions must To find the inverse of a To find the inverse of a A B 0 ) Find A D 8 7 C 7 D 6 5 ) Find BC ) Find DB ) Find the determinant of A. 5) What are the dimension of matri B? 6) What is E(F + G) if E = [ ] ; F = [ 6 0 ] ; G = [5 ]? 6 7) Calculate 8 6? 9

10 8) Calculate 6? 9) Calculate 0 6? 8 8 0) Use your calculator to find the inverse of [ ]. Give all elements as fractions ) Find A - when A + 5y = 9 ) Solve { using matrices. + y = 5 ) Solve 5y z 5 z z 0 using matrices. y z 5 0