FUNCTIONS (1.1) 2. Use the graph at the right to find the following. Assume the domain is 3 x 11. A. Find f (0). B. On what interval(s) is f( x)

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1 FUNCTIONS (.). As you travel at a constant speed from Tucson to Bisbee, you pass through Benson. Sketch possible graphs to represent the functions below. Label the aes and any important features of your graphs. A. distance from Tucson as a function of time B. distance from Benson as a function of time C. distance from Bisbee as a function of time D. speed as a function of distance. Use the graph at the right to find the following. Assume the domain is A. Find f (). B. On what interval(s) is f( ) increasing? C. Find so that f( ) =. D. Find the zeros of f( ). D. What is the range of f( )? f() The relationship between the tuition, T, and the number of credits, c, at a particular college is given by + c c 6 Tc () = 8 + ( c 6) 6 < c 8 A. What is the tuition for 7 credits? B. If the tuition was $, how many credits were taken? C. Give a practical interpretation of the vertical intercept. D. Give a practical interpretation of the slope. 5. Sketch H( α) H ( α t) =. Label the aes and the intercepts clearly. The constants are positive. o 6. Solve g( y ) = 5 for g( y) 6 = y. t A. Find the domain of f() t = t + t 8. B. Create a function that has a domain of (4, ). 8. Gasoline is being pumped into a tank at a constant rate (cubic feet per minute). A graph of the height of the gasoline in the tank as a function of time is shown. You can assume the tank was initially empty and the tank will be filled. Determine a possible shape of the tank. Height Time

2 EXPONENTIAL FUNCTIONS (.). Find a formula for each. A. A computer purchased for $ loses roughly % of its value each year. B. A kitchen appliance purchased for $ loses roughly $8 in value every two years. C. The amount of a pollutant increases eponentially at a continuous rate of.4% per year.. Find a formula for each graph. y y (,.5) (, 8.75) (,.474) (-,.48). It is predicted that the population of a particular city will triple by the year 6. Determine the annual, monthly, and continuous growth rates. Epress your final answers as percents. 4. Determine which table illustrates an eponential function and which one illustrates a linear function. Find formulas for these two functions. Table A f( ) Table B h ( )

3 NEW FUNCTIONS FROM OLD (.). Give values so that the table represents an invertible function m 4 5 f( m ) For what values of A and K will S() t At K = be a one-to-one function?. The life epectancy, L, of a child can be modeled by the function below. The variable y is the year of birth in relationship to 99. For eample, y = corresponds to 99. y Ly ( ) =.y +. A. Find L () and give a practical interpretation. B. Find L (78) and give a practical interpretation. 4. Let f( ) = and + g ( ) = +. Find f ( g ( )) and g( f( )). Simplify completely. 5. Consider two functions h ( ) and f( ). Let h ( ) = and the graph of f( ) is at the right. 7 A. Is h ( ) even, odd, or neither? B. Find h( f ()). f(5) f() C. Find. 5 f( ) Suppose (, 5) is a point on the graph of y = f( ). Find the corresponding point in each of the following transformations. A. y = f ( ) B. y = f( ) + 7. Suppose an oil spill covers a circular area and that the radius increases according to t rt () = 4+ where t represents the number of minutes since the spill was first observed. A. What was the radius of the spill when it was first observed? B. Determine the eact time when the area of the spill was 8π.

4 LOGARITHMIC FUNCTIONS (.4) nt. Derive the tripling time formula for P= Pa. What does this tripling time depend on?. Let S( D).59.8log ( D) = + where S is the slope of a beach and D is the average diameter (in mm) of the sand particles on the beach. Suppose a particular beach rises 9 meters for every meters inland. What size sand would you epect to find on that beach?. Sketch a graph of each function. Include the domain. A. 7 log 7 y = B. ln y = e 4. You and a friend plan to purchase cars in October. The initial value of your car will be $4, and will depreciate 7% each year. The initial value of your friend s car will be $6,5 and will depreciate % each year. You agree to echange cars when their values are equal. A. How long do you need to wait? Give an eact value and a decimal value to the nearest month. What is the value of your car? B. What would your depreciation rate have to be in order for the values of the cars to match at the end of 7 years? Assume your friend s car still depreciates % each year. 5. Find the domain, range, all intercepts, and asymptotes for gt ( ) = log (5t+ 6). 6. A. Solve for w: ln( w) + ln( w+ ) = ln() B. Solve for : log( + ) = + log( )

5 TRIG FUNCTIONS (.5). The rate of intake during a respiratory cycle for a person at rest is proportional to a sine wave with period si seconds. Suppose the rate is.85 liters/sec when t =.5 sec. A. Find an equation that describes the rate of intake as a function of time. B. Graph one cycle of your equation. Indicate the part that corresponds to inhaling.. The temperature in a room is given by Tt ( ) = C+ Asin( Bt ( 8)) where t is measured in hours since midnight. Find values for A, B, and C if the function describes temperature fluctuations over a 4 hour period, the average temperature in the room is 7, and the greatest difference in temperature is 9.. Find the eact value of each. π π A. cos B. cot 4 6 C. sec () D. arcsin 4. A positive angleθ in standard position has its terminal side in Quad III. If tanθ =, find sinθ Solve for the angle so that angle < π. In each case there are two solutions. A. sinθ = B. tan β = C. secα is undefined 6. Solve for the variable (if possible) so that variable π. Epress your answer in radians. A. + tan y = B. sin y cos 6 t = C. sin( ) cos( ) = 7. Find the eact value for csc tan. Your answer will be in terms of. 8. Epress the area of this triangle in terms of A, b, and c only.

6 POLYNOMIAL & RATIONAL FUNCTIONS (.6). Consider the function y ( ) = A. Plot yin ( ) the window 4, 5 y. B. Find the zeros of y. ( ) C. Epress yin ( ) factored form.. Create a possible equation for the polynomial shown below Create equations of rational functions with the following characteristics: A. A horizontal asymptote of y = and a vertical asymptote of = 4. B. No horizontal and no vertical asymptotes. 4. Use the graphs below to answer the following: f( ) g ( ) h ( ) (,6) (,5) (,-8) To answer the questions below, it would be helpful to find the equations of each function above. A. Find a possible formula for B. Find a possible formula for f( ) m ( ) =. Find all asymptotes and intercepts of m. ( ) g ( ) q ( ) =. Find all asymptotes and intercepts of q. ( ) h ( ) ( )

7 LIMITS AND CONTINUITY (.7 &.8). Determine the values where each graph below is discontinuous and find a possible equation In each case sketch a graph with the given characteristics. A. f (4) is undefined B. f () = C. f () = and lim f( ) = and lim f( ) doesn t eist and lim f( ) = 4. Find each of the limits. Use the limits to sketch an accurate graph. Label all important characteristics. A. f( ) = lim f( ) lim f( ) lim f( ) lim f( ) + lim f( ) B. g ( ) = e lim g ( ) lim g ( ) lim g ( ) + lim g ( ) 4. Find the value of k that would make the function continuous in each case. sin(5 π ) e A. g ( ) = B. h ( ) = k = k = 5. Find the value(s) of k that would make the limit eist. Find the limit(s). 6 + k A. lim B. lim k + 6. Let + cos( π ) f( ) = 5 > + A. Find so that f ( ) =. B. What graphical feature occurs at =?