(2) Find the domain of f (x) = 2x3 5 x 2 + x 6

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1 CHAPTER FUNCTIONS AND MODELS () Determine whether the curve is the graph of a function of. If it is state the domain and the range of the function. 5 8 Determine whether the curve is the graph of a function of. If it is, state the domain and range of the function. in words what the graph tells ou abou race? Did each runner finish the race? (m) 00 A () Find the domain of f () = The graph shown gives the weight of a certain person as a function of age. Describe in words how this person s weight varies over time. What do ou think happened when this person was 30 ears old? 3. The graph shows the power consumpt ber in San Francisco. ( P is measured i sured in hours starting at midnight.) (a) What was the power consumption (b) When was the power consumption the highest? Do these times seem r P weight (pounds) The graph shows the height of the water in a bathtub as a function of time. Give a verbal description of what ou think happened. height (inches) (3) Find the domain and sketch the graph of 5 { 0 3 f () = if < 5 if age (ears) time (min). You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a table. Describe how the temperature of the water changes as time passes. Then sketch a rough graph of the temperature of the water as a function of the elapsed time.. Three runners compete in a 00-meter race. The graph depicts the distance run as a function of time for each runner. Describe 4. Sketch a rough graph of the number o function of the time of ear. 5. Sketch a rough graph of the outdoor te of time during a tpical spring da. 6. Sketch a rough graph of the market va function of time for a period of 0 ea well maintained. 7. Sketch the graph of the amount of a pa sold b a store as a function of the pri 8. You place a frozen pie in an oven and ou take it out and let it cool before ea temperature of the pie changes as time rough graph of the temperature of the 9. A homeowner mows the lawn ever W Sketch a rough graph of the height of time over the course of a four-week pe 0. An airplane takes off from an airport a another airport, 400 miles awa. If t re utes since the plane has left the termin

2 V r 4 3 r 3given. Find a function that represents the amount of air curve. required to inflate the balloon from a radius of r inches to a 47. The line segment joining the points, 3 and 5, 7 radius of r inches. 48. The line segment joining the points 5, 0 and 7, 0 8 Evaluate the difference quotient for the given function. 49. The bottom half of the parabola 0 plif our answer. (4) Find an epression for the function whose graph is the given curve. f 3 h f The top half of the circle 4 f 4 3, h f a h f a f 3, h f, f 3, 33 Find the domain of the function. f 4 9 f t s 3 t f f a a f f 30. f t t s3 t s t Find a formula for the described function and state its domain. 53. A rectangle has perimeter 0 m. Epress the area of the rectangle as a function of the length of one of its sides. 54. A rectangle has area 6 m. Epress the perimeter of the rectangle as a function of the length of one of its sides. (5) At the surface of the ocean, the water pressure is the same as the air pressure above the water, 5lb/in. Below the surface the water pressure increases b 4,34lb/in. for ever 0 ft of descent. (a) Epress the water pressure as a function of the depth below the ocean surface. (b) At what depth is the pressure 00lb/in. (6) Solve questions,, 3 (pages 36 and 37) from our book.

3 of f is given. Write equations for the graphs (c) 3 f (d) f 4 rom the graph of f as follows. (e) f 6 pward. ownward. the 6 the left.! the -ais. the -ais. ll b a factor of 3. ll b a factor of 3. graph is obtained from the graph of f. 3 f $ # (b) (d) f 8 f 8 _6 _ (f) 8f ( 8 ) f is given. Match each equation with its % _3 asons for our choices. (b) f 3 (7) The graph of f () is given. Write each equation for the graphs given below. 3 ilable in TEC (8) Find f g h, where f () =, g() = and h() =. (9) Find f and g such that ( f g) =

4 4 47. H H sec 4 (s ) 50. Use the table to evaluate each epression. (0) Use the table given, if(a) necessar, f t below(b) tot evaluate f each(c) epression. f f (a) ( f g)()= (b) (g f )()= (c) ( f f )(4)= (d) ( f g )() = (e) (g g )() = () Simplif (63 ) 4 5. (d) t t (e) t f 3 (f) f t 6 5. Use the given graphs of f and t to evaluate each epression, or eplain wh it is undefined. (a) f t (b) t f 0 (c) f t 0 (d) t f 6 (e) t t (f) f f 4 0 g H s f t f shoreline. The ship is 6 km from shore house at noon. (a) Epress the distance s between the as a function of d, the distance the noon; that is, find f so that s f d (b) Epress d as a function of t, the tim that is, find t so that d t t. (c) Find f t. What does this function 56. An airplane is fling at a speed of 350 one mile and passes directl over a rad (a) Epress the horizontal distance d ( has flown as a function of t. (b) Epress the distance s between the station as a function of d. (c) Use composition to epress s as a f 57. The Heaviside function H is defined b H t 0 if t if t It is used in the stud of electric circui sudden surge of electric current, or vol instantaneousl turned on. (a) Sketch the graph of the Heaviside (b) Sketch the graph of the voltage V t switch is turned on at time t 0 a instantaneousl to the circuit. Writ terms of H t. (c) Sketch the graph of the voltage V t switch is turned on at time t 5 se () Find the domain of f () = e e.

5 (3) Under ideal conditions a certain bacteria population known to double ever three hour. Suppose that there are initiall 00 bacteria. (a) What is the size of the population after 5 hours. 5 (b) What is the size of the popuation after t hours. (c) Estimate the size of the population after 0 hours.

6 6 (4) Find a formula for the inverse of the function. (a) f () = (b) f () = e + e. (c) f () = ln( + 3).

7 7 (5) Find the eact value of each epression. (a) log (6) log (5) + log (0) (b) e ln5 (c) ln (lne ) e 0 (6) Solve < ln < 9 for.

8 8 (7) Let f () = 3 e. (a) Find the domain of f. (b) Find f. (c) Find the domain of f.

9 0 CHAPTER LIMITS AND DERIVATIVES. Eercises. Eplain in our own words what is meant b the equation (8) If a ball is thrown into the air with a velocit of 40 ft/s, its height in feet t seconds later is given b = 40t 6t f 5 l. (a) Find the average Is velocit possible for the this statement time period to be true beginning and et f when 3? t = and lasting 4 Eplain. (i) 0.5 second. Eplain what it means to sa that (iii) 0.05 second l f 3 and (ii) 0. second (iv) 0.0 second l f 7 (g) t 9 (h) t t t l 4 4 In this situation is it possible that l f eists? Eplain. 3. Use the given graph of f to state the value of each quantit, if it eists. If it does not eist, eplain wh. (a) f (b) f (c) f l l l (d) f l 5 (e) 4 f 5 6. For the function h whose graph is giv quantit, if it eists. If it does not eis (a) h (b) h ( (d) h 3 (e) h ( (g) l 3 h l 0 (j) h (h) (k) l 3 l0 h 0 h l5 (b) Estimate the instantaneous velocit when t =. 4. For the function f whose graph is given, state the value of each quantit, if it eists. If it does not eist, eplain wh. (a) f (b) f (c) f l 0 l3 (9) For the function f whose graph is given, l 3 state the value of each quantit, if it eists. If it does not eist, eplain wh. (d) f (e) f 3 l _4 _ Sketch the graph of the function and values of a for which l a f eists f if if if f sin cos sin if 0 if 0 if (a) 0 f ()= (b) 3 f ()= 5. For the function t whose graph is given, state the value of each quantit, if it eists. If it does not eist, eplain wh. (a) t t (b) t t (c) t l 0 (d) t t (e) t t (f) t t t l t l 0 t l t t t l 0 t l ; 9 Use the graph of the function f to st it, if it eists. If it does not eist, epla (a) f l 0 (b) f l 0 9. f 0. f e (c) 3 + f ()= ; Graphing calculator or computer with graphing software required. Homework Hints available in TEC (d) 3 f ()= (e) f (3)=

10 0 (0) Sketch the graph of an eample of a function f that satisfies the following conditions: f () =, f () =, f () =, f (0) = and f (3) = SECTION.3 CALCULATING LIMITS USIN. Given that find the its that eist. If the it does not eist, eplain wh. (a) (c) (e) l () The graph of f and g are given. h l Use them to evaluate each f it, if it eists. If the it does not eist, eplain wh.. The graphs of f and t are given. Use them to evaluate each (a) [ f () + g()] (b) [ f () + g()] (c) [ f ()g()] 0 (d) f () g() (e) [ 3 f () ] (f) 3 + f ().3 Eercises (b) (d) (f) it, if it eists. If the it does not eist, eplain wh. (a) (c) (e) 3 7 Evaluate the it and justif each step b indicating the appropriate Limit Law(s). (b) (d) (f) ( s 3 ) =ƒ l l 8 f 4 l f 5t l sf l t f t l f t l0 3 f l l 3 8. (a) What is wrong with the following equation? (b) In view of part (a), eplain wh the equation is correct. t l 6 6 l t 3 l 3f l t t h f t l l s3 f l t 3 t 3 5 t l su 4 3u 6 ul 3 = f t 3 l h 0 l Evaluate the it, if it eists l l5 5 t t l 3 t 7t 3 4 h h l 0 h l l s.. l t l 0 ts t t ; 5. (a) Estimate the value of b graphing the function f (b) Make a table of values of f fo the value of the it. (c) Use the Limit Laws to prove that ; 6. (a) Use a graph of l0 f s 3 s3 to estimate the value of l 0 f (b) Use a table of values of f to es decimal places. (c) Use the Limit Laws to find the e ; 7. Use the Squeeze Theorem to show th l 0 cos 0 0. Illustrate b f, t cos 0, and screen. ; 8. Use the Squeeze Theorem to show th s 3 sin l0 Illustrate b graphing the functions f of the Squeeze Theorem) on the same l l h l h l t

11 () Evaluate each it, if it eists. 4 (a) (b) h 0 ( + h) 4 h (c)