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
. Evaluate lim 4 b) ( + 44)( ) c) 4 d) 4 4 e) 4 6. Find the limit: lim 0 + 0 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) = 7+ 9. 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( ) = 00+ 400. The demand equation is p = 00 0. 0. 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+ 6= 0. b) c) d) e) 4
( + ) ( ) 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. 4 9 9 = 9 9 b) A = 4 c) 9 9 9 9 9 9 = e) The inverse does not eist. 4 9 9 A A A 9 9 = 4 9 9. If A =, find 4 A 4 A 9 4 = b) c) A = 8 7 d) A 4 6 = e) 8 6 A = 4 9 4 A = 6 9 6. 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)
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
. 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( ) = 06. + 400. 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
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 0 0.00 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 ( ) 0. 0. 6 + 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+ 86.90 c) Q= 0 p+ 04 d) Q= 0 p04 e) Q = p 04 0 6
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 =. = 0786. b) = c) = d) = 6 e) =. 48 0. 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) 4 4 4 7 4 7 0 0 c) 0 7 d) 0 7 e) 4 4 4 4 7
0. Given A =, B = 0 and C = 4 8, 0 7 9 4 6 7 4 8 9 4 6 b) find ( ) AB + C 6 7 9 0 7 c) 9 8 9 8 8 9 6 d) 6 6 0 0 e) 4 0 0 6 9 66 7 4 8. The function f ( ) = 4 8 + 8 + 88 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 0 0 0 40 00 0 0 0 TV 0 8 0 6-0.04 b) -0.89 c) -0.9989 d) 0.89 e) 0.9989 8
. A complete graph of ( ) 4 f = + + 0 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