Math 2003 Test D This part of the Exam is to be done without a calculator

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1 Math 00 Test D This part of the Eam is to be done without a calculator. Which of the following is the correct graph of =? b) c) d) e). Find all the intercepts of = -intercept: 0 -intercepts: 0, -, b) -intercepts: -, -intercept: 0 c) -intercepts: -, no -intercept d) -intercepts: 0, -, -intercept: 0 e) -intercepts: -, no -intercept b) =. If f ( ) =, then f ( ) c) f ( ) = d) f ( ) ( ) = e) ( ) 4. The slope of the line tangent to the curve + 4 =6 at the point (, ) is 7 b) c) d) e) 7

2 . Evaluate lim 4 b) ( + 44)( ) c) 4 d) 4 4 e) 4 6. Find the limit: lim b) c) d) e) 7. Determine the values of, if an, at which the tangent to the graph of 4 = + has a horizontal tangent. ( ) = 0 b) = 0 and = c) = 0 and = d) = e) There are no values of for which the graph of has a horizontal tangent. ( ) ( )( ) 8. Find an equation of the tangent line to f = 4 at (, 0). = 7+ b) = 7 c) =7 d) = 7+ e) = The radius, r, of a circle is decreasing at a rate of 4 centimeters per minute. Find cm the rate of change of the area, A, in when the radius is cm. min 0π b) 00π c) 00 π d) 40π e) 40 π 0. Find f ( ) if f ( ) ( ) 6 = +. ( ) = ( + ) b) ( ) = ( + ) 6 c) ( ) ( ) f f 8 d) ( ) = ( + ) e) f ( ) ( ) f = + f = 8 +. For a production level of units of a commodit, the cost function in dollars is C( ) = The demand equation is p = What price p will maimize the profit? $00 b) $0 c) $900 d) 00 e) $6000. Find the -coordinate of the center of the circle = 0. b) c) d) e) 4

3 ( + ) ( ) f h f. For the function f ( ) = 6, find lim h 0 h 0 b) c) 48 d) 48 e) 48 d) 4. If A =, find the inverse, 4 A = 9 9 b) A = 4 c) = e) The inverse does not eist A A A 9 9 = If A =, find 4 A 4 A 9 4 = b) c) A = 8 7 d) A 4 6 = e) 8 6 A = A = Find the average rate of change of the function ( ) f 7 closed interval 4. 4 b) 7 c) 6 d) 4 e) 4 = + + on the + 8 = consists of a line and a hole. Find the 9 equation of the line and the coordinates of the hole. =, 7 7. The graph of f ( ) line: hole: ( ) b) line: = hole: (, 0) c) line: = hole: ( 9, 0) d) line: = hole: ( 9, 7) e) line: = 9 hole: (, 7)

4 8. The table below shows some values for the function f. If f is a linear function, what is the value of a + b? f() a 0 b b) 4 c) 48 d) 64 e) It cannot be determined from the information given. e) 9. Write an equation of the line parallel to the line = through the point (, 6). = + 4 b) = 4 c) = + d) = 6 = 4 = is not 6 + continuous. Which of the discontinuities are removable? No points of discontinuit b) Discontinuit at = (removable); Discontinuit at = (nonremovable) c) Discontinuit at = (non-removable); Discontinuit at = (nonremovable) d) Discontinuit at = (removable); Discontinuit at = (removable) e) Discontinuous onl at = (non-removable) 0. Find the values (if an) for which the function f ( ). For the demand function defined b p+ = 00 for 0 and the suppl function p =4 for 0, the market equilibrium price is: 76 b) 70 c) 7 d) 8 e) 4. The function whose equation is f = 4+ has a graph which is a parabola whose verte is:, b) ( ), c) 9 ( ) ( ) (, ) d) (, 9) e) (, ) 4

5 . Which of the following define functions that are odd? I. = + II. = + III. = I onl b) II onl c) III onl d) I and II e) II and III 4. The demand function and cost function for units of a product are defined b 60 p = and C( ) = Find the marginal profit when = 00. $. per unit b) $4.8 per unit c) $9.0 per unit d) $87. per unit e) $.6 per unit 4. For the rational function f ( ) =, the horizontal asmptote is: 4 = and = b) = and = c) = 4 d) =4 e) There is no horizontal asmptote

6 Math 00 Test D Some of the problems on this part of the eam require a calculator 6. In the figure below, line l passes through the origin and intersects the graph of a, 04.. What is the slope of line l? = at the point ( ) =^(-) (a, 0.4) line l b) 0.0 c) 0.8 d) 0. e).0 7. Evaluate the following limit if the limit eists: lim h 0 b) 0 c) 8 ( ) h 6 h d) 8 e) 8. At a price of $.0 per gallon, the weekl demand b consumers for gas is 4 gallons. If the price rises to $. per gallon, the weekl demand drops to 9 gallons. Find a formula for Q, the weekl quantit of gas demanded in terms of p, the price per gallon, assuming that the demand is linear. Q= 0 p86.90 b) Q= 0 p c) Q= 0 p+ 04 d) Q= 0 p04 e) Q = p

7 9. Let f be the function defined b ( ) f = + +. Find the value of for which the average rate of change of f on the interval = to = is equal to the instantaneous rate of change on the interval from = to =. = b) = c) = d) = 6 e) = Let f ( ) = and g( ) =. For what values of is g( ) f ( ) f ( ) > g( ) for all values of. b) g( ) > f ( ) for all values of. c) > 0 d) > e) > >?. The following represents the sstem of equations AX = B = 7 4 z 4 In order to solve the sstem it is necessar to evaluate: 0 7 b) c) 0 7 d) 0 7 e)

8 0. Given A =, B = 0 and C = 4 8, b) find ( ) AB + C c) d) e) The function f ( ) = has vertical asmptotes at: Nowhere b) = onl c) = onl d) = and = e) = and = 4. The table below shows the IQ of ten students and the number of hours of TV each watch per week. Find the correlation coefficient for the data. IQ TV b) c) d) 0.89 e)

9 . A complete graph of ( ) 4 f = is: b) c) d) e) Answers to Test D ) b ) d ) e 4) b ) d 6) b 7) d 8) d 9) d 0) c ) b ) b ) e 4) c ) b 6) a 7) d 8) d 9) b 0) b ) a ) e ) e 4) a ) c 6) b 7) c 8) c 9) a 0) d ) c ) b ) d 4) b ) c 9