 # Calculus Questions

## Transcribed Text

Question 1: (1 point) Classify the following function as even, odd, or neither: (a) Even (b) Odd (c) Neither Question 2: (1 point) Identify all curves below which are the graph of a function . (a) 1/12 x5+3x2 = )x(f )x(f = y (b) (c) (d) (e) 2/12 (f) Question 3: (1 point) Consider the functions . (a) What is the domain of (Remember to type infinity for and -values that are NOT in the domain of . Note that the domain of and the domain of are both __________,__________ (b) From the list below, select all (a) 0 (b) 10 (c) 13 (d) 9 (e) 12 (c) From the list below, select all (a) 0 (b) 16 (c) 6 (d) 15 (e) 5 . ? .) -values that are NOT in the domain of . 3/12 gf801+x12−2x=)x(g57+x02−2x=)x(f f g x g f x ∞ g⋅f =x =x =x =x =x =x =x =x =x =x )( )∞ ,∞−( Question 4: (1 point) Determine and given and below. (Remember to type sqrt(x) for .) __________ __________ Question 5: (1 point) The number of bacteria living on a plate of food is given by: , The temperature of the food when left out on a picnic table in the summer sun is given by where is the time in hours. (a) Find the composition . __________ (b) How long does the food need to be left out in order for the bacteria population to hit exactly 10,400? ____________ hours where is the temperature of the food in degrees Celsius. Question 6: (1 point) Let . (a) Sort the following operations in the order they are applied to in (Click and drag) null (b) Consider the inverse function . Sort the following operations in the order they would be applied to in null (c) What is the inverse function ? __________ 4/12 )x(1− f x )x(1−f )x(1− f )x(f x 02≤t≤0 ,01+t 4=)t(T 02≤T≤1−002+T04−2T01=)T(N 1− − − − x− √ = ) x ( g 4 + x3 = )x(f −x−√ )x()f ∘ g( )x(g )x(f )x()g ∘ f( ))t( T( N 8 − − + − x − 5 − 6√ = ) x ( f =)x(1− f t T = )x()f ∘ g( = )x()g ∘ f( Question 7: (1 point) Hooke's Law described the relationship between the force needed to extend (or compress) a spring and how much the length of the spring compresses (or extends) from the springs equilibrium length. This relationship is given by where is a constant, is the force, and is the displacement from equilibrium. (a) How would we describe the relationship between and ? (a) Quadratic (b) Linear (c) Inversely Propotional (b) For a particular spring, a force of 8.5 Newtons causes the spring to compress by 0.01 meters. What must the value of spring correct to 2 decimal places? ____________ be for this Question 8: (1 point) The ideal gas law describes the relationship between the pressure , volume , temperature , and number of moles of gas particle for an ideal gas. It is given by where is known as the gas constant. (a) Suppose pressure and number of moles are held constant. Rewrite the ideal gas law so that temperature is a function of volume. __________ (b) How would we describe the relationship between temperature and volume? (a) Proportional (b) Inversely proportional Question 9: (1 point) An object is dropped from a height of 580 m above the surface of a planet. The following table shows the height of the object at certain times. Time, s Height, m 5/12 k TRn= VP )T( )V( )P( R )n( ht xk = F xF xFk = ) V( T 0 580 1 578.205 2 572.82 3 563.845 4 551.28 5 535.125 6 515.38 The path of the object can be modeled using a quadratic function of the form (a) Using the information in the table above, determine the value of the constant ____________ (b) Determine the value of the constants and , correct to 2 decimal places. ____________ ____________ exactly. (c) Using the information above, determine when the object will hit the ground, correct to 1 decimal places. ____________ (d) The table below gives a list of planets and their respective accelerations due to gravity. The constant in your equation above is equal to half the magnitude of the acceleration, i.e. . Determine the planet where the object is dropped. Body Magnitude of the Acceleration due to gravity, m/s2 Mercury 3.59 Venus 8.87 Earth 9.81 Mars 3.77 Jupiter 25.95 Saturn 11.08 Uranus 10.67 Neptune 14.07 (a) Mercury (b) Venus (c) Mars (d) Jupiter (e) Saturn (f) Uranus (g) Neptune 6/12 a c c+tb+ 2ta = )t(h g |a|2 = g ba =b =a =c Question 10: (1 point) Identify the graph of (a) where: (b) (c) (d) 7/12 3 − 3 + x = )x(h 1 )x(h = y Question 11: (1 point) Identify the graph of where: (a) (b) (c) 8/12 |01 − 3x| = )x(k )x(k = y (d) Question 12: (1 point) Solve the following expression for : ____________ Question 13: (1 point) Starting with the graph of 1. Reflect about the x-axis 2. A shift of 9 units down 3. A shift of 1 units left __________ , write the equation of the graph that results from the following transformations: Question 14: (1 point) The graph of the function is shown below. 9/12 nx= 1 5−x−√ n 7 )9x( 3x= )x( f xe = )x(y = )x(y =n Which of the following is the graph of the inverse function ? (a) 10/12 )x(1− f (b) (c) 11/12 (d) 12/12

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