Calculus Questions

1 What is the slope of the normal to y x 2 x 2 at 2 0

0 10 For which values in the domain is this graph decreasing Give your answer in interval notation Assume the graph extends to infinity in both directions Try again 1 00 Edit my response

10 For which values in the domain is this graph decreasing Give your answer in interval notation Assume the graph extends to infinity in both directions 110 Submit

Write your answer in interval notation 2x 4x 0 2 0

x 2y 4 7x 2y 8 Find the solution Give the answer as an orde pair

No Calculator Be sure to show some work or give an explanation lems 8 1 If the line tangent to the graph of the function fat the point 1 7 passes through the point 2 2 then f 1 is A 5 B 1 A 0 2 If f 3 8 and f 3 4 then f 3 02 is approximately A 7 88 B 7 92 C 7 98 D 8 02 B C 3 19 D 7 3 A particle moves along the x axis so that at time t 0 its position is given by x t 2t 21t 72t 53 At what time t is the particle at rest A t 1 only B t 3 only C t only 0 24 2 724 53 Name Shannon Dineen Date 10 03 23 B 5 5 If f is a continuous function defined by f x E Undefined 24 1 1 19 t 1 58 t 1 0 4 1 2 19 53 0 10242 19 53 0 421 4 What is the slope of the line tangent to the curve 3y 2x 6 2xy at the point 3 2 c 7 D E C 4 E 8 08 D t 3 and t 1 1 7 2 x bx x 5 5 sin Ex x 5 D 4 E 3 and t 4 then b E 5

X Given that f x 3x 4 and g x x 1 find 2f x g 2

Solve the quadratic by completing the square Show work WILL be required on the exam x 12x 32 0 Solution 1 Solution 2

The figure shows graphs of f f f and f Identify each curve a b c d bv f av f bv f YA X

The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon SA cm s 20 0 10 20 T C What is the meaning of the derivative S T OS T is the maximum sustainable speed of Coho salmon for a given temperature OS T is the rate of change of the maximum sustainable speed of Coho salmon with respect to the speed of Coho salmon OS T is the rate of change of the maximum sustainable speed of Coho salmon with respect to the temperature OS T is the rate of change of the temperature with respect to the temperature OS T is the rate of change of the temperature with respect to the maximum sustainable speed of Coho salmon

X y 20 99 30 17 119 150 15 117 b Find the equation of the line containing the first and the last data points y 4x 179 Type an equation Type your answer in slope intercept form Use integers or fractions for any numbers in the equation c Graph the line found in part b on the scatter plot Choose the correct graph below OA 0 14 129 10 139 OB 30 150 001 0 ON O C 30 150 00 O D 30 156

The quantity of oxygen that can dissolve in water depends on the temperature of the water So thermal pollution influences the oxygen content of water The graph shows how oxygen solubility S varies as a function of the water temperature T SA mg L 16 12 8 4 8 16 24 32 40 TCC What is the meaning of the derivative S T OS T is the rate at which oxygen solubility changes with respect to the oxygen solubility OS T is the rate at which temperature changes with respect to the temperature OS T is the rate at which oxygen solubility changes with respect to the water temperature OS T is the rate at which temperature changes with respect to the oxygen solubility OS T is the current level of oxygen solubility for a given temperature 0

The cost of producing 2 ounces of gold from a new gold mine is C f x dollars a What is the meaning of the derivative f 2 What are its units Of x is the rate of change of the production cost with respect to the number of ounces of gold produced Its units are dollars per ounce Of x is the average production cost with respect to the number of ounces of gold produced Its units are dollars per ounce Of x is the total production cost Its units are dollars Of x is the total amount of gold produced Its units are ounces b What does the statement f 700 13 mean O The total cost to produce 13 ounces of gold is approximately 700 O After 13 ounces of gold have been produced the average production cost is 700 ounce So the cost of producting 13 ounces is about 700 ounce O After 700 ounces of gold have been produced the average production cost is 13 ounce So the cost of producing 700 ounces is about 13 ounce After 700 ounces of gold have been produced the rate at which the production cost is increasing is 13 ounce So the cost of producing the 700 th or 701 st ounce is about 13 c Do you think the values of f x will increase or decrease in the short term What about the long term Explain In the short term the values of f x will Select an answer of start up costs as a increases But eventually f x might operations because more efficient use is made Select an answer due to large scale

For the data given below answe ants 6 7 11 13 X Y 2 3 3 5 4 5 9 46 6 y 2 0357 x 1 3214 Type integers or decimals rounded to four decimal places as needed e What is the correlation coefficient r r 0 996 Type an integer or decimal rounded to three decimal places as needed f Use a graphing utility to draw the scatter plot and graph the line of best fit on it Choose the correct graph below OA Q 8 15 Xmin 0 Xmax 20 Xscl 2 Ymin 0 SOB 5 Xmin 0 Xmax 20 Xscl 2 Ymin 0 OC Xmin 0 Xmax 20 Xscl 2 Ymin 0 Vmov 0 Vede O D Q 15 3 Xmin 0 Xmax 20 Xsc Ymax 20 Ysd 2

The number N of locations of a popular coffeehouse chain is given in the table The numbers of locations as of October 1 are given Year 2004 2005 2006 N 2007 2008 8571 10245 12625 15015 16682 a Find the average rate of growth between each pair of years locations year 2004 to 2006 2006 to 2007 2005 to 2007 locations year locations year b Estimate the instantaneous rate of growth in 2006 by taking the average of the last two rates of change in part a locations year c Estimate the instantaneous rate of growth in 2006 by measuring the slope of the secant line through 2005 10245 and 2007 15015 locations year d Estimate the instantaneous rate of growth in 2007 by measuring the slope of the secant line through 2006 12625 and 2008 16682 locations year Compare the growth rates you obtained in part c and d What can you conclude O The rate of growth is decreasing O There is not enough information O The rate of growth is constant

The quantity in pounds of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q f p a What is the meaning of the derivative f 7 O The rate of change of the quantity of coffee sold with respect to the price per pound when the price is 7 per pound The rate of change of the price per pound with respect to the quantity of coffee sold when the price is 7 per pound O The price of the coffee as a function of the supply O The rate of change of the price per pound with respect to the quantity of coffee sold O The supply of coffee needed to be sold to charge 7 per pound b What are the units of f 7 O pounds dollar Odollars pound Odollars pound pound O pounds dollars pound Odollars pounds

For f x a fog 6 X 5 and g x b gof b g of x 5 find the following composite functions and state the domain of each c fof X Type your answer innervai notation Use integers of actions for any numbers in the expression your answer c f of x 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression d gog The domain of g ofis 5 U 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression your answer 6 x 5 31 5x Simplify your answer Use integers or fractions for any numbers in the expression 31 The domain of fofis co 5 U 5 5 31 5 Type your answer in interval notation Use integers or fractions for any numbers in the expressic your answer d go g x Simplify your answer Use integers or fractions for any numbers in the expression

The limit represents the derivative of some function f at some number a State such an f and a 1 h 1 h lim h 0 f x x x a 1 Of x x x a 0 Of r r a 2 Of x x a 0 Of x 26 a 1

f x In x 3 b Graph f Choose the correct graph A 10 G B 7 C c From the graph determine the range and any asymptotes of f The range of f is 0 00 Type your answer in interval notation OA The vertical asymptote of f is x Simplify your answer OB There is no vertical asymptote 10 Q Determine the vertical asymptote of f if it exists Select the correct choice and if necessary complete your choice

Determine whether f 0 exists x sin f x Of 0 does not exist Of 0 does exist QUERY if x 0 if x 0

For f x a fog 6 X 5 and g x b gof 5x b gof x X 1 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression find the following composite functions and state the domain of each c fof d gog The domain of fog is 0 U 0 1 U 1 00 Type your answer in interval notation Use integers or fractions for any numbers in the expressio your answer c fo f x 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression The domain of g of is 5 U 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expressic your answer 6 x 5 31 5x Simplify your answer Use integers or fractions for any numbers in the expression The domain off of is Type your answer in interval otation Use integers or fractions for any numbers in the expressic your answer

Find f a f t 6t 14 t 6 To find f a we will use the formula f t f a t a f a lim t a Since f t 6t 14 t 6 f a lim t a we have 6t 14 t 6 6a 14 a 6 t a Simplifying everything we get f a lim

If the tangent line to y f z at 7 5 passes through the point 0 4 find f 7 and f 7 f 7 f 7 Question Help Message incto

The limit represents the derivative of some function f and some number a State such an f and a cos h 1 h lim h 0 Of x cos x a 0 Of x cos 2 a 4 Of x cos r a 3 Of x cos x a Of x cos z a 6

Find an equation of the tangent line to the curve at the given point y 49 7 To find the equation of a line we need the slope of the line and a point on the line Since we are requested to find the equation of the tangent line at the point 49 7 we know that 49 7 is a point on the line So we just need to find its slope The slope of a tangent line to f x at x a can be found using the formula f x f a Ha mtan lim G In this situation the function is f x Therefore we have y mtan lim x 7 lim 249 249 Using the factorization 49 7 x 7 we have x 7 2 49 7 x 7 So we found the slope and we know that 49 7 is a point on the line Substituting these values into the point slope formula y yo m o and solving for y we can conclude that the equation of the tangent line to f x at x 49 is zia f x f a HIP man lim and a

K f x In x 3 a Find the domain of f The domain of f is 3 00 Type your answer in interval notation to answer parts a through f b Graph f Choose the correct graph OA 110 Q Q M OB 40 Q Q L C c From the graph determine the range and any asymptotes of f The range of f is Type your answer in interval notation 40 10

Find f a f x 4x 4x 1 f a

For f x a fog 6 X 5 5 and g x find the following composite functions and state the domain of each X b gof c fof 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression d gog The domain off og is 0 U 0 1 U 1 0 Type your answer in interval notation Use integers or fractions for any numbers in the expression S your answer b gof x 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression The domain of g ofis 5 U 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression S your answer c f of x 6 x 5 31 5x Simplify your answer Use integers or fractions for any numbers in the expression The domain off of is Type your answer in interval notation Use integers or fractions for any numbers in the expression Si your answer

Strontium 90 is a radioactive material that decays according to the function A t Age 0 024 amount present and A is the amount present at time t in years Assume that a scientist has of strontium 90 a What is the decay rate of strontium 90 b How much strontium 90 is left after 20 years c When will only 200 grams of strontium 90 be left d What is the half life of strontium 90 a The decay rate of strontium 90 is Type an integer or a decimal Include the negative sign for the decay rate

d Use a graphing utility to find the line of best fit y 2 0357 x 1 3214 Type integers or decimals rounded to four decimal places as needed e What is the correlation coefficient r Type an integer or decimal rounded to three decimal places as needed

For f x a fog 6 X 5 and g x b gof 5 X b gof x 1 find the following composite functions and state the domain of ea c fof d gog 6x a fog x 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression The domain off og is 0 U 0 1 U 1 00 Type your answer in interval notation Use integers or fractions for any numbers in the expres your answer 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression The domain of g ofis 5 U 5 00 Type your answer in interval notation Use integers or fractions for any numbers in the expre your answer c f of x Simplify your answer Use integers or fractions for any numbers in the expression

7 grams Do not round until the final answer Then round to the nearest thousandth as needed

K For f x a fog 6 X 5 5 and g x find the following composite functions and state the domain c x b gof c fof d gog a fog x 6x 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression The domain of fog is 0 U 0 1 U 1 00 Type your answer in interval notation Use integers or fractions for any numbers in the exp your answer b g of x 5X 25 6 Simplify your answer Use integers or fractions for any numbers in the expression The domain of g of is Type your answer in interval notation Use integers or fractions for any numbers in the exp your answer

3x x 7 2 0 12 OA B Use the formula x b b 4ac 2a with a What is the solution set b and c 2 Rewrite the equation so the constant term is on the right side and the coefficient of x is equal to 1 Add Then take the square root and isolate x 1 to both sides and factor the left side as a perfect spare 36 2 Write the equation in the form x p by moving the constant term and x term to the right side of the equation and then dividing both sides by solve for x D Set the equation equal to 0 and factor the nonzero side of the equation Set each factor equal to 0 and solve The solution set is Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Take the sp

Write a balanced equation for the double replacement precipitation reaction described using the smallest possible integer coefficients A precipitate forms when aqueous solutions of copper II iodide and potassium hydroxide are combined Be sure to include states such as s or aq

Solve the equation by completing the square 1 3 4 64 0 How is the equation solved by completing the square Select the correct choice below and if necessary fill in the answer box es within your choice O A Use the formula x b b 4ac 2a with a b and c OB Rewrite the equation so the constant term is on the right side Add to both sides and factor the left side as a perfect square Then take the square root and is OC Write the equation in the form x p by moving the constant term and x term to the right side of the equation Then take the square root to solve for x OD Set the equation equal to 0 and factor the nonzero side of the equation Set each factor equal to 0 and solve

Ay y 20 2 3 3 5 4 6 20 c Graph the line found in part b on the scatter plot Choose the correct graph below O A 5 9 17 6 11 7 8 13 15 O B 20 0 20 d Use a graphing utility to find the line of best fit y 2x 1 Type integers or decimals rounded to four decimal places as needed 20 20

x 6x 55 How is the equation solved by completing the square Select the correct choice below and if necessary fill in the answer box es within your choice O A Use the formula x 2 b b 4ac 2a with a b and c OB Add to both sides and factor the left side as a perfect square Then take the square root and isolate x 2 OC Write the equation in the form x p by subtracting from both sides and then take the square root OD Set the equation equal to 0 and factor the nonzero side of the equation Set each factor equal to 0 and solve

Solve the equation by completing the square 1 12 3x X O A 0 How is the equation solved by completing the square Select the correct choice below and if necessary fill in the answer box es within your choice Use the formula x b b 4ac 2a with a b and c OB Rewrite the equation so the constant term is on the right side and the coefficient of x is equal to 1 Add take the square root and isolate x to both sides and factor the left side as a perfect square O C Write the equation in the form x p by moving the constant term and x term to the right side of the equation and then dividing both sides by solve for x OD Set the equation equal to 0 and factor the nonzero side of the equation Set each factor equal to 0 and solve Take the square rota

X y 20 2 3 3 5 X 4 6 20 5 9 A 6 11 a 7 13 y ZA 1 Type an equation Type your answer in slope intercept form Use integers or fractions for any numbers in the equation c Graph the line found in part b on the scatter plot Choose the correct graph below O A rough f 8 15 OB Ay 20 20 d Use a graphing utility to find the line of best fit y 0x 0 Type integers or decimals rounded to four decimal places as needed C 20 04 0 X 20 OD 20 Ay 0 20 COU

K For f x a fog 6 X 5 5 and and g x find the following composite functions and state the domain of each b gof c fof d gog a fog x 6x 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression The domain off og is Type your answer in interval notation Use integers or fractions for any numbers in the expression Si your answer

K The function f x x 2 is one to one a Find the inverse of f and check the answer b Find the domain and the range of f and f c Graph f f1 and y x on the same coordinate axes a f x x 2 Simplify your answer Use integers or fractions for any numbers in the expression b The domain of f is 0 00 Type your answer in interval notation The range of f is 00 Type your answer in interval notation The domain of f is 0 00 1 Type your answer in interval notation The range of f is 0 00 Type your answer in interval notation c Graph f f1 and y x on the same coordinate axes The graph of y x is shown using da Choose the correct graph O A O C Q Q B D

9x 1 a Find its inverse function f and check your answer b Find the domain and 1 a f x X 9x 8 Simplify your answer b The domain of f is Type your answer in interval notation Use integers or fractions for any numbers

K The function f x 6x 2 is one to one a Find the inverse of f and check the answer b Find the domain and the range of f and f c Graph f f1 and y x on the same coordinate axes x 2 6 a f x Simplify your answer Use integers or fractions for any numbers in the expression b The domain off is 00 Type your answer in interval notation The range of f is 0 00 Type your answer in interval notation The domain of f is 0 00 Type your answer in interval notation The range is 0 00 Type your answer in interval notation c Graph f f and y x on the same coordinate axes of f1 Question Viewer

Use transformations to graph the function f x 2 2 Determine its domain range and horizontal asymptote D Horizontal compression or stretch E Horizontal shift F Vertical compression or stretch Use the graphing tool to graph the function What is the domain of f x 2 The domain of f x is 0 00 Type your answer in interval notation What is the range of f x 2 2 The range of f x is 0 00 Type your answer in interval notation What is the horizontal asymptote of the given function F The horizontal asymptote is the line Type an equation E 10 B 6

K Consider the functions f x 9x 1 and g x x 1 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other AI Use a comma to separate answers as needed B No values should be excluded from the domain b What is g f x g f x x Simplify your answer Give any values of x that need to be excluded from g f x Select the correct choice and if box within your choice OA x Use a comma to separate answers as needed B No values should be excluded from the domain c Are the functions f and g inverses of each other Choose the correct answer O Yes O No

transformations to graph the function f x 2x 2 rmine its domain range and horizontal asymptote ch transformations must be applied to obtain the graph x 2x 22 Select all that apply A Vertical shift B Reflection about the x axis C Reflection about the y axis D Horizontal compression or stretch E Horizontal shift F Vertical compression or stretch se the graphing tool to graph the function What is the domain of f x 2x 2 The domain of f x is Type your answer in interval notation 10 B 6 4 2 10 Ay 8 6 4 2 2 6 8 40 INT L

6x and g x 4x 6 evaluate the following expressions 4 b gof 2 c fof 1 c fof 1 d gog 0 3 4 420 Simplify your answer f 2 582 Simplify your answer f 1 36 Simplify your answer g 0 Simplify your answer

tion f x x3 2 is one to one he inverse of f and check the answer he domain and the range of f and f f f and y x on the same coordinate axes x 2 your answer Use integers or fractions for any in the expression domain of f is 0 00 ur answer in interval notation ge of f is ur answer in interval notation

Consider the functions f x 9x 1 and g x x 1 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other a What is f g x f g x x Simplify your answer Give any values of x that need to be excluded from f g x Select the correct choice and if necessary fill in the box within your choice A x Use a comma to separate answers as needed B No values should be excluded from the domain b What is g f x g f x Simplify your answer