1. For each of the following, state the domain and range and whether the given relation defines a function. b)

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1 Eam Review Unit 0:. For each of the following, state the domain and range and whether the given relation defines a function. (,),(,),(,),(5,) a) { }. For each of the following, sketch the relation and complete the chart. domain range Intervals of increase Intervals of decrease Absolute maimum Absolute minimum -intercept -intercept(s). State the transformations applied to the original function and then graph the given function. a) ( ) 5. Suppose the graph of a function f() is given. Describe how the graph of f is related to the graph of f(). 5. Determine the inverse of each function. a) {,),(,),(,),(7,) } ( 5 d) f ( ) ( ) 5. a) Graph the function f ( ). State the domain and range of f(). Determine the equation of the inverse of f(). d) Graph the inverse of f() on the same grid. e) Is the inverse of f() a function? f) State the domain and range of the inverse of f(). 7. Simplif using the laws of eponents. Epress answers with positive eponents.

2 a) ( )( ) Factor full. a) d) e) f) g) h) i) j) k) l) n) o) m) ( ) p) q) s) ( ) ( ) r) 9. Simplif full. State restrictions in c and d. 8 a) 7 a a a 8 5 d) e) a a a 5a 5 5 f) g) m m m m 5m m 0. For the function 7 5, a) calculate the average rate of change of with respect to from to. calculate the instantaneous rate of change of with respect to at. Unit :. Sketch each of the following functions, labelling the -intercepts. a) ( )( )( 5) ( ) ( 5)( 7). Divide. (a) ( 9 5) ( ) ( ( ) ( ) ( ( 5 5) ( ). When a certain polnomial is divided b, the quotient is 5 and the remainder is. What is the polnomial?. Find the remainder when 7 0 is divided b 5. Is 5 a factor of 7 0? Eplain. 5. When k is divided b the remainder is, determine the value of k.

3 Unit :. Simplif and state restrictions. 7 a) 8 a 7a a a a a a 9 d) 8 9 a a 5ab 5b ab 5b a a ab b ab b. State the equations of an vertical asmptotes for the following functions. a) g ( ). State the equations of an horizontal/oblique asmptotes and the coordinates of an intersection points. 5 a) m ( ). Solve each inequalit. a) ( -)( 5)( -) 0 > 5 5 d) 0 e) > 0 f) g) 0 9 h) < For each of the following functions, a) state the domain. determine the and -intercepts. determine the equations of an vertical asmptotes and the behaviour of the function near these asmptotes. d) determine the equation of an horizontal or oblique asmptotes and the coordinates of an points where the graph crosses this asmptote. e) sketch the function using this information. i) iii) j ( ) ii) h ( ) iv) f ( ) k ( ) 8 7 v) 5 p ( ) vi) g ( ) ( )

4 . A construction worker drops a bolt while working on a high-rise building 0m above the ground. After t seconds, the bolt has fallen a distance of s metres, where s ( t) 0 5t, 0 t 8. a) What is the average velocit for the interval t 8? What is the velocit at t seconds? 7. Suppose that ou have an rational function. Eplain how ou would do the following: a) Find the domain of the function. Locate the intercepts of the function, if an. Test for smmetr (is it even, odd or neither). d) Determine the equations of the vertical asmptotes. e) Determine the equations of an horizontal/oblique asmptotes and the coordinates of an intersection points. f) Determine where the graph is above the -ais and where it is below the -asis. 8. Create a rational function that has all of the following characteristics: a. Crosses the -ais at b. Touches the -ais at - c. One vertical asmptote at and another at d. One horizontal asmptote at - Unit :. Convert to degree or radian measure as appropriate, to the nearest hundredth. 5 a) 75 0 d). Draw the two special triangles, labeling the angles in ratians and degrees!. The coordinates of the point P on a terminal arm of an angle θ, in standard position, are P(5, - ), where 0 θ. Determine the eact values of sin θ, cos θ, and tan θ.. Find the eact value of each trigonometric epression. 5 a) sin 7 5 sec tan d) csc 7 9 e) sin cos tan 7 f) sin cos

5 5. Complete the chart. Equation amplitude period Phase shift sin ( ) cos. Sketch one ccle for each of the following functions. State the domain and range. a) sin( ) cos sin( ) d) cos e) sec f) csc g) cot h) tan. Graph two complete ccles of the function. 8. Determine an equation for the function g(t). 7. Determine the period of the function sin( ) 9. A weight is hanging on a large spring, originall at a height of 8 in. from the top of the table. If ou pull down on the spring, until it is onl in. off the table and let go, it will begin to oscillate from that minimum height of in. to a maimum height of in. If it makes one bounce in seconds, give the equation for h(t) height above the table after letting go. 0. The terminal arm of an angle θ lies in Quadrant III on the line with equation 5 0. Calculate θ to the nearest degree. 5

6 . A crank of length 0 cm, starting from an initial horizontal position P, rotates counterclockwise at a uniform rate of one revolution per second. Unit : a) Determine a function that gives the height of the end of the crank from the initial position line at an time t. How far is the end of the crank from the initial line in 0.7 s? At what time(s) between 0 and is the crank cm from the initial position line?. Solve each equation on the interval 0. a) sin sin 0 sin sin d) tan 0 e) cot sin cot f) sin cos 0. Prove each identit. a) tan - sin (sin )(tan tan ) sec sin sin sin cot csc d) sin cos tan cos e) cosθ sinθ sinθ cosθ f) tan t tan t sec t sec t g) tan t tant tant h) cot cos cot cos i) ( tan ) sec tan j) ( cost ) sin t cost cost sint sint. Determine the eact value for each of the following epressions. a) tan sin 8 cos 7 sin(t ). Is sint an identit? Eplain.

7 5. Epress each of the following as a single trigonometric ratio. θ θ a) sincos cos sin sin. If cos and, determine the eact value of each of the following 5 epressions. a) csc sec tan Unit 5:. Evaluate each of the following eactl. Use laws of eponents and logarithms and show our work! a) log log d) log e) log 7 log 5 log f) 89 g) 5 9 ( ) ( ) log h) 5 5 ( ) 7 j) log ( 8) k) log ( ) log log 9 i) log7. Solve for. Answers should be eact where possible, otherwise round to decimal places. a) 7log()5 log( ) log( ) log( ) log (7) 0 d) log( ) e) log log( ) f) log ( 5) log( ) log( ) g) log( 8 ) log( ) h) log () i) log () log ( ) j) log (log ()) k) log ( ) (log ()) l) 7 m) 8 n) / o) 8 p) 0 7

8 q) 0 5 r) ( ) 50 s) (5 ) 5 5 t) ,000 u) 50(.0) 000 v) ( ) 9( ) 0 w) 7 9 ) ( ) ) 5( 0 ) z) ( ). Graph each function. Label the coordinates of the ke point and the equation of the asmptote. State the domain and range of the function. 5 log ( ) a) ( 7 ). If ou start a biolog eperiment with 5,000,000 cells and 5% of the cells are ding ever minute, how long will it take to have less than,000 cells? 5. If a radioactive substance has a half-life of 00 ears, how long will it take for the substance to deca to 0% of its initial amount?. If Jonl, Iowa had a population of 0,000 in 95 and a population of 5,000 in 99, how large was the population in 90 assuming an eponential population model? 7. Earl in the centur the earthquake in San Francisco registered 8. on the Richter scale. A recent earthquake in San Francisco measured 7. on the Richter scale. How man times more intense was the earlier San Francisco earthquake? 8. If one earthquake is 5 times as intense as another, how much larger is its magnitude on the Richter scale? 0.95t 9. The growth of a colon of bacteria is given b the equation 0e. If there are initiall 500 bacteria present and t is given in hours determine each of the following. (a) How man bacteria are there after a half of a da? ( How long will it take before there are 0000 bacteria in the colon? 0. Suppose that a small countr has a population of 0 million and an annual growth rate of.5%. How long will it take before the population doubles?. If an average whisper measures 0 db and the threshold of pain is at 0 db, Determine the actual difference in intensit between the two sounds.. Compared to a ph of 7, what is the ph value for a liquid with,000 times more hdrogen ions? 8

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