Functions Questions and Answers

et B be the region of the xy plane bounded by y x 1 y 2 2 and z 2 Find the total area of the region B b Set up an integral representing the volume of the solid which has it s base contained in the egion B if it s known that cross sections of the solid perpendicular to the z axis are squares You on t need to evaluate the integral

Find the limit 5x 91 9 lim 2 x 3x 10

Perform the indicated operations with expressions involving radicals and then simplify x 5 x 5

Rewrite the expression with positive exponents x y z 0 Simplify your answer completely xy 6 0

Select all the expressions equivalent to 410 A 25 22 B 220 C 44 46 D 47 4 3 E 44 4 6 2019 Illustrative Mathematics All Rights Reserved Select all that apply OA B Oc

3 10 points Find the maximum rate of change of f x y xy at the point 1 3

Jan TOJ TROG Find the exact value of cos K in simplest radical form M 4 6 20 K

Tansit company operates commuter trains to help people get to the city ch day Each train travels on a straight route to and from the farthest ation stopping at other stations along the route he graph shows the distance y miles the train is from the station after minutes Distance from the Station miles Commuter Train Distance 30 25 10 5 0 10 20 30 40 50 60 70 80 Time minutes Formula Sheet Calculator Re Type your answer in the box You may use numbers a decimal point and or a negative sign in your answer Based on the graph what was the average speed in miles per minute the train during the interval of 30 to 40 minutes

1 point Find the maximum and minimum values of the function f x y 2x 3y 4x 5 on the domain x y 16 The maximum value of f x y is List the point s where the function attains its maximum as an ordered pair such as 6 3 or a list of ordered pairs if there is more than one point such as 1 3 4 7 The minimum value of f x y is List points where the function attains its minimum as an ordered pair such as 6 3 or a list of ordered pairs if there is more than one point such as 1 3 4 7

Let f t be the weight in grams of a solid sitting in a beaker of water Suppose that the solid dissolves in such a way that the rate of change in grams minute of the weight of the solid at any time t can be determined from the weight using the forumula f t 4f t 6 f t If there is 1 grams of solid at time t 2 estimate the amount of solid 1 second later

For the given cost function C z 78400 800x 1 First find the average cost function Use it to find a The production level that will minimize the average cost b The minimal average cost

H 4 3 2 1 4 3 2 1 Y 1 2 3 What is the slope of the line 1 2 32 30

What is the value of 36x 8y2 when x 3 and y 6 OA 288 OB 180 O C 1 200 O D 3 600

2 Consider the function below On the closed interval a b at how many points is the Mean Value Theorem satisfied 3 At how many points on the closed interval are the conditions of the Mean Value Theorem satisfied for f x cos 2x sin x

Suppose you are analyzing a company with the following characteristics If the risk free is 3 and the expected market risk premium is 6 what is this company s WACC Answer in percent showing two decimal places Market value of debt 500 million Market price of each share 20 Number of shares outstanding 75 million Tax rate 18 The average yield on current debt pre tax cost of debt 4 Beta 1 5

How many gallons of a 70 antifreeze solution must be mixed with 90 allons of 15 antifreeze to get a mixture that is 60 antifreeze Use ne six step method Strength Gallons of Solutions 70 15 60 X 90 x 90 Gallons Antifree

Write the equation for the function in the form y Atan Br D or y A cot Br D y 2 10 10 10 2T 6TT 8TT 10T 12 H

Write the equation of the function in the form y A sec Br D or y A csc Ba D 10 10 11 12 CSC 11 0

2 This question is based on the following graph Price 5 00 4 00 3 00 2 00 1 00 0 B D Quantity 12 G M 16 20 a Construct a table for points A from the data shown in the graph b According to economists price is the independent dependent variable and quantity is the variable c Write a linear equation that summarizes the data

Question 31 1 po 4 Listen aved 40 How long will it take a colony of bacteria that double every three weeks to grow from 7000 cells to 23 000 cells a just under 4 weeks b just over 5 weeks Oc exactly 4 weeks d 2 months Question 32 1 point 40 Listen Saved Evaluate the following expression 2log 64 a

Question 27 1 point Listen Which statement is TRUE for the graph of the exponential function f x 2 Saved a The graph only exists to the right of the y axis Ob There is a vertical asymptote c There is no restriction on the range d The graph only exists above the x axis Question 28 1 point 4 Listen Saved Rewrite the equation logs0 100 z in exponential form a 80 100

Listen The relationship between the functions f x and g x 3 is a They are reflections of each other in the x axis b They are reflections of each other in the y axis Oc They are reflections of each other in the line y x d They are not related to each other Question 8 1 point Listen Saved Rewrite and simplify log as a logarithm with base ten 10 a 2log102

Find the linearization of the function f x y 96 3x 2y2 at the point 4 4 L x y Use the linear approximation to estimate the value of f 3 9 3 9

How many nonnegative integer solutions are there to the equation 2x1 2x2 x3 x4 12

For a given input value uuu the function hhh outputs a value vvv to satisfy the following equation 4u 8v 3u 2v 4 u 8v 3u 2v 4 u plus 8 v equals minus 3 u plus 2 v Write a formula for h u h u h left parenthesis u right parenthesis in terms of uuu

1 point Find the vector equation for the line of intersection of the planes 4x 5y 5z 3 and 4x 5z 2 r 0 25

Let VV be the vector space P3 x P3 x of polynomials in xx with degree less than 3 and WW be the subspace W span 5 3x x2 7 5x a Find a nonzero polynomial p x p x in W p x b Find a polynomial q x q x in V W q x

4 Sense making of Derivative Rules through finding areas Use the area concept to explain the power rule x 2 2x and product rule fg f g fg This will be important when we prove the Fundamental Theorem of Calculus Hint Square with sides X and rectangle with sides f and

Estimate the area under the graph of f x x 3x 1 over the interval 2 1 using four approximating rectangles and right endpoints Rn Repeat the approximation using left endpoints Ln Report answers accurate to 4 places Remember not to round

Perform the row operations on the matrix and write the resulting matrix Replace R by R R 206 2 28 OA O C 20 11 20 6 OB O D 20 00 O 01

a Find the equation of the straight line through 1 2 and 3 4 b Find the equation of the line through 8 8 with slope 8 c Find a point that lies on both of the lines in a and b a Find the equation of the straight line through 1 2 and 3 4 Type an equation b Find the equation of the line through 8 8 with slope 8 Type an equation c Find a point that lies on both of the lines in a and b Simplify your answer Type an ordered pair

Match each function with its graph which is one of those shown Drag each of the equations given above into the appropriate area below depending on whether it represents the graph of the function 9 9 by 6 6 1 991 hv 1 661 Q G Q Q G 9 9 by 6 6 1 991 hv1 661 5 ATTR Q 9 9 by 6 6 1 991 hv 1 661 oo a 5 9 9 by 6 6 1 991 hwl 661 O O C Time Remaining 02 24 4

Graph the following functions on the same axes a f x 2 b g x 2x 3 c h x 2x 2 d If c is a positive constant explain how the graphs of y 2 and y 2 are related to the graph of f x 2 SIDE Choose the correct graph to the right X C The graph of y 2 is the same as the graph of y 2 shifted graph of y 2 is the same as the graph of y 2 shifted by c The by c SCIID OA WW Food Hicks O C G 23 OB O D Q

Graph the polynomial P x 3x 2 x 1 x 2 OA S OB erme OC Q O D

Find the value of the expression log 32 O A A OB O C 4 35 3 32 54 O D w

Without graphing find the x and y intercepts for f x f x x 7x 7 Select the correct choice below and fill in any answer boxes in your choice OA There is no x intercept B The x intercept s are Type an integer or decimal rounded to the nearest tenth as needed Use a comma to separate answers

70 60 50 40 30 20 10 10 10 10 20 30 40 50 Luca is a lifeguard and spots a drowning child 50 meters along the shore and 70 meters from the shore to the child Luca runs along the shore for a while and then jumps into th water and swims from there directly to the child Luca can run at a rate of 3 meters per second and swim at a rate of 1 1 meters per second How far along the shore should Luca run before jumping into the water in order to save the child Round your answer to three decimal places

thout graphing describe the shape of the graph of the function and complete the ordered pairs 0 and 1 70 3x A The graph lies below the x axis rises from left to right with the negative x axis as a horizontal asymptote 0 1 and 1 73 B The graph lies above the x axis rises from left to right with the negative x axis as a horizontal asymptote 0 1 and 1 70 C The graph lies below the x axis falls from right to left with the negative x axis as a horizontal asymptote 0 7 and 1 7 D The graph lies above the x axis falls from left to right with the negative x axis as a horizontal asymptote 0 7 and 1 70

There is less than 1 200 difference between the tuition at State University and Highbrow College The tuition at Highbrow is 4 500 Express this as an absolute value inequality Use x for the tuition of State Universit OA x 4 500 1 200 OB x 1 200 4 500 OC x 4 500 1 200 OD x 1 191

e revenue function R x and the cost function C x for a particular product are given These functions are valid only for the specified range of values Find the number of units that must oduced to break even R x 200x x C x 10x 7800 0 x 100 GELED

Determining Whether an Integer Satisfies an Inequality Jan 06 12 59 36 PM Which of the following values are solutions to the inequality 5 6x 8 None II only I and II 4 I 4 II 3 II and III O I only III only I and III O I II and III III 5 Submit Answer

Jan 06 10 59 45 AM Jin took a taxi from his house to the airport The taxi company charged a pick up fee of 2 10 plus 4 75 per mile The total fare was 116 10 not including the tip Which equation could be used to determine m the number of miles in the taxi ride 116 1 4 75 2 1m 1161 21 m 4 75 4 75 2 1m 116 1 m 1 116 1 4 75 2 1

College Fund When Marcus started high school his grandmother opened a college savings account On the first day of each school year she deposited money into the account 1000 in his freshman year 600 in his sophomore year 1100 in his junior year and 900 in his senior year The account earns interest of r at the end of each year When Marcus starts college after four years he gets the balance of the savings account plus an extra 500 a If r is the annual interest rate of the bank account the at the end of the year the balance in the account is multiplied by a growth factor of x 1 r Find an expression for the total amount of money Marcus receives from his grandmother as a function of this annual growth factor x

Fabian took a taxi from his house to the airport The taxi company charged a pick up fee of 3 plus 2 25 per mile The total fare was 43 50 not including the tip Which tape diagram could be used to represent the context if m represents the number of miles in the taxi ride A B C D A 3 3 3 3 B 3 3m 3m 3 2 25 41 25 43 5 2 25 41 25 3 3 43 5 Submit Answer 2 25m 2 25 2 25 2 25m 2 25 2 25 2 25 2 25

a 1 More on Polynomials Question 4 f x x 3 Which information is true about f x Select one O O O f x is neither even nor odd f x is odd f x is even O We need more information to determine if f x is even or odd

De More on Polynomials Question 6 Which of the following statements is true about this function Select one f x O O 1 X f x is odd f x is even O f x is both even and odd Of x is neither even nor odd O We cannot determine whether f x is even or odd

Select one Ox 14x 14x 16 2x 14x 7x 4 4x 7x 7x 1 x 7x 14x 8 De which expression could be f x De De O O O

Select one 09 More on Polynomials Question 5 f x x Which information is true about f x O f x is neither even nor odd O We need more information to determine if f x is even or odd f x is odd O f x is even

11 How does increasing the c value from 0 to 7 translate the graph Why

The function is graphed below State the values that fulfil the If there are no such values type DNE If there are multiple discrete values separate them with commas If there are a whole Interval of values that fulfill the requirement use Interval notation to give all of the values in the Interval Type oo for co and oo for oo Also type U for U y 1 5 2 2 1 5 0 7 0 2 0 5 1 2 1 1 5 1 0 5 0 0 5 Where is f at 1 1 0 1 5 1 24 Where is f 0 Vz in the Interval 0 7 0 2 Where is 0 Vz in the Interval 0 5 What are the values in the closed interval 1 2 1 5 where f undefined at z What are the critical values of f at z 1 1 5 Image developed from imago at Svesen KH Where does have local minimums What are these local minimum values the relative minimum is occurs at x Where does have local maximums the relative maximums occur at z which Where does have absolute minimums What are these absolute minimum values the absolute minimum is occurs at I occurs of I which Where does have absolute maximums What are these absolute maximums values the absolute maximum is which