Functions Questions and Answers

4 The quadratic y x 6 x 8 passes through which of the following points 6 X 6 11 10 2 1 5

Bae is willing to pay up to 160 for a particular pair of boots She can buy the boots for 120 The marginal cost of producing the boots is 70 Which of these is TRUE regarding the economic surplus associated with her purchase of the boots Consumer surplus is 90 and producer surplus is 120 Consumer surplus and producer surplus are the same Consumer surplus is 50 and producer surplus is 40 Consumer surplus is 40 and producer surplus is 50

Prove the given identity tan x sec x csc x cot x Choose the correct proof below OA tan x sec xcsc x sin x 1 1 cos x cos x sin x sin x cos x 1 sinx sin x cos x 2 COS cot x O C tan x sec xcsc x sin x COS X 1 sin x sin x cos x COS X sin x cos x cot x OB O D tan x sec x sin x cos x sin x cos x 1 sin X sin x cos x cos x cot x tan x sec X 1 cos sin x cos X 1 sinx sin x cos x 2 COS X sin x cos x cot x

3 Given the equation y 8 cos 7x 6 5 find a 5 pts the amplitude b 5 pts the period c 5 pts the horizontal shift and direction d 5 pts the midline

Solve the given equation log 2x 1 log x 3 1 X Type an integer or a decimal Round to two decimal places as needed Use a comma to separate answers as needed

2x y 20x Type an exact answer using radicals as needed Question 8 of 20 Simplify Assume that no radicands were formed by raising negative quantities to even powers 2x y 20x

Prove the given identity sin x sec x cos x csc x sec xcsc X Choose the correct proof below OA sin xsec x cos xcsc x 1 sin x cOS X sin x cos x sin x cos x 1 sin x cos x sec xcsc x cos X sin x OC sin x sec x cos x csc x 1 cos x sin x cos x 1 sin x sin x cos x 2 sin x cos x 1 sec x csc x www OB sin x sec x cos xcsc x 1 sin x cos X sin x cos x 2 sin x cos x sin x cos x 1 sec x csc x OD sin x sec x cos x csc x 1 sin x cos X COS X 2 sin x cos x sin x cos X 1 sin x cos X sec x csc x

Solve the given equation 0 9 2x Question 1 of 20 The solution s is are x Round to three decimal places as needed Use a comma to separate answers as needed

I am told that a house will cost 250 000 in 5 years because of a 6 rate of inflation What should the house cost toda O a 186 814 O b 197 455 O c 201 989 O d 222 765

Joe s shoe store had sales last year of 4 000 800 He had cost of goods sold of 1 800 700 He had nothing to depreciate what was his taxable income O a 1 800 700 O b 2 200 100 O c 4 000 800 O d 5 810 500

Use the formula to answer the question The price of your dream vacation home is 178 000 The cost of the home is financed with a 15 year fixed rate mortgage at 3 9 Use this information to find the amount of your monthly payment Round your answer to the nearest cent PMT 1 307 74 12 177 54 4 571 37 579 09 P 1 1 nxt

You want to have 120 000 in an account after 40 years for your retirement Your investment counselor suggests that you make regular monthly deposits into an annuity that pays 4 25 interest compounded monthly Find the amount that must be deposited monthly rounded to the nearest cent Periodic Deposit P 1 40 95 2 68 39 3 288 90 4 171 nxt 4 95 34

For the quadratic function f x a The x coordinate of the vertex is 3x 6x 1 answer parts al through Type an integer or a simplified fraction b The y coordinate of the vertex is N Type an integer or a simplified fraction c The graph of f opens Type up or down 2

Find real numbers a b and c so that the graph of the function y the points 1 2 3 9 and 0 3 The value of a is 1 4 The value of bis 5 4 The value of Cis 3 ar bx c contains Type integers or simplified fractions

alyze the graph of the function R x 1 What is the domain of R x 2 What is the equation of vertical asymptote s of R x A xlx 0 B xlx 5 5 C xlx 0 25 D x x 5 E All real numbers 3x 10 x 25 A x 0 B x 5 5 C x 0 25 D x 5 E There is no vertical asymptote For part 1 the answer is Type a letter For part 2 the answer is 3 What is the equation of the horizontal or oblique asymptote of Rx Ay 0 B y 1 Cy 10 D y x E There is no horizontal or oblique asymptote

Write as the sum and or difference of logarithms Express powers as factors In x 1 8x x 913 X 9 In 4 In x In 1 8x In 3 In x 9 In 4 In x 5ln 1 8x 3ln x 9 In 4 In x In 1 8x 3In x 9 4In x In 1 8x 3ln x 9 Page 38 of 41

rm a polynomial f x with real coefficients having the given degree and zero Degree 3 zeros 1 i and 7 f x x3 5x 14x 12 f x x 5x 12x 14 x3 f x x3 x 12x 14 f x x3 7x 12x 12

with a score I that satisfies the inequality particular test a normal score is 600 It can be shown that anyone 600 2 54 has an unusual score Determine the scores that would be considered unusual 14 Test scores between 564 44 and 635 56 would be considered unusual Only test scores greater than 635 56 would be considered unusual Only test scores less than 564 44 would be considered unusual Test scores less than 564 44 or greater than 635 56 would be considered unusual

ind all zeros of the function and write the polynomial as a product of linear factor f x x 6x 12x 24x 32 f x x iB x i x 2 x 2 f x x 1 x 8 x 2i x 2i f x x 2 x 4 x 2 x 2 Of x x 2 x 4 x 2i x 2i

the rational zeros theorem to find all the real zeros of the polynomial function f x x 2x 5x 6 Write each zero in a separate box N

The function f x 10 is one to one Find the Inverse of f x 10 3 Of s 1 V Of 1 2 3 10 T f 1 x V 10 3 x 10

Find the C coordinate of the points of intersection of the graphs of two functions f x x g x 2x I OI x 11x 24 I C 1 3 18 2 r 12x 18 3 x 2 Ox 3 x 2 10 18 2 T 10

Determine the quadratic function whose graph is given below 10 4 4 Of x 22 0 12 10 x x 8x 12 2

be constructed from a square sheet of plastic by removing a of side 3 inches from each corner and then turning up the sides If the box must have a volume of 675 cubic inches find the length of one side of the open box 21 in 15 in 18 in 14 in Page 22 of 41

poden access ramp is being built to reach a platform that sits 30 Inches above the floor The ramp drops 2 Inches for every 31 Inch run y Flatiom S 30 Ramp X Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform Oy 1 x 30 31 Oy r 20 T bcam 30

get a grade of C the average of the first five tests scores must be greater than or lass you have scores of 68 73 71 and 90 on the first four of five tests To equal to 70 and less than 80 Solve an inequality to find the least score you can get on the last test and still earn a C 68 48 90 59 Page 18 of 41

Marty s Tee Shirt Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front There are fixed costs of 560 to set up for production and variable costs of 31 per jacket Write an equation that can be used to determine the total cost C x encountered by Marty s Company in producing x jackets C x OC x 560x 31 31x 560 G r 31560

Solve the equation 5 X 5 e solution is 3 X 3 24 x 5 x 3 17 of 41

ph of a function fis given Use the graph to answer the question For what numbers x is f x 0 100 100 y 100 60 70 60 O 60 70 100 100

1 1 1 1 a The local minimum occurs at x A 40 b The local maximum occurs at x

Graph the function 1 0 f x 2 3 220 O 6 6 6 6 X 6

nd and simplify the difference quotient of f for the function f x x 5x 1 1 2x h 5 2x 2x 2xh h h 2 h 2x h 1

is thrown vertically upward from the top of the building 448 feet tall with an initial velocity of 56 feet per second Its height h in feet after t seconds is given by h t 448 56t 16t2 After how long will it take for the ball to reach its maximus height Round your answer to 1 decimal place 4 9 sec 15 6 sec O 1 8 sec 8 2 sec

y1 8 23 8 31 8 y1 4 3 4 y 1 4 1 8 23 8 31 8 1 4 3 4 y 1 4 Simplify your answer Use positive exponents only

Verity the identity cos x cos x tan x secx Choose the sequence of steps below that verifies the identity O A O B O C cos x cos x tan x cos x tan x 1 cos x cos x tan x cos x 1 tan x cos x cos x tan x cos x 1 tan x OD cos x cos x tan x 1 tan x secx 1 sec x 1 2 sec x 1 sec x secx sec x secx sec x sec x sec x

1 Solve the following equations Round your answers to 3 decimal places 10 pts ea a 9 531 441 I b 400 600 600 e 0 5x Give exact answers do not round 10 pts ea

s Campus smoking areas Outlook iz 2 K DZL Homepage 23F Technology Mathemati tan r r t v mylab pearson com P Pearson MyLab and Mastering Question 8 of 10 Simplify the given expression The result will be one of sin x cos x tan x cotx secx or csc x tan x cot x CSC X

Prove the given identity sec xcsc x sin xsec x cos x csc x Choose the correct proof below OA sec xcsc x sin xsec x 1 cos x sin x sin x cos x 1 sin X sin x cos x cos x cos xcsc x 1 COS X sin x OC sec xcsc x sin xsec x 1 1 cos x sin x sin x cos x 1 sin x sin x cos x 2 COS X cos X CSC X Question 8 of 10 O B sec xcsc x sin xsec x 1 1 This quiz 25 This questia cos x sin x 1 sin 2 sin x cos x 2 COS X X sin x cos x cos x csc x OD sec xcsc x sin xsec x 1 1 sin x cos x sin x 1 sin x sin x cos x cos 2x sin x cos x cos xcsc X 1 COS

Use a double angle formula to find the exact value of the given expression 2 3 2 cos Question 6 of 10 H This question 2 cos Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Factor and simplify csc x csc x sec 2 X Choose the correct simplification below D A tan x sec x B 1 C sin x sin 2 X

Activity 7 Mathematical Induction Part 2 Solve the following problems 1 Expand the following sums 10 a 3 b i 3 5 i 5 ST 2i i 2 NI c 1 1 Pre Calculus

2 15 Find the solution to the initial value problem dy 2 esin x cos x y y 0 t by finding an appropriate integrating factor No credit for any other method dx

Assignment 10 Problem 3 1 point A triangle is defined by the points A 7 7 9 B 10 4 5 and C 3 k 9 The area of the triangle is 16390 Determine the value of k k 0 or k 0 this problem

Prove the given identity sec x csc X sin xsec X cos XCSC X Choose the correct proof below OA sec xcsc x sin xsec x 1 COS X sin x 2 1 sin x sin x cos x 2 COS X sin x cos x cos X CSC X OC sec xcsc x sin xsec x sin x cOS X sin x cos x 2 1 sin x sin x cos x 2 COS X cos x CSC X Question 10 of 10 D OB sec xcsc x sin xsec x 1 This quiz 25 poll This question 3 COS X sin x 1 sin X sin x cos x cos x sin x cos x cos xcsc x K sin x OD sec xcsc x sin x sec x 1 1 cos x sin x sin x cos x 1 sin x sin x cos x 2 COS x COS XCSC X sin x 1 COS X 1 cos x

Question 3 of 10 Simplify the given expression The result will be one of sin x cos x tan x cotx secx or csc X tan x cot x sin x tan x cot x sin x

1 Points DETAILS LARPRECALCRMRP7 3 1 062 Consider the following function f x 2x ex 1 a Use a graphing utility to graph the function y 0 4 3 2 50 The function is decreasing on 40 30 20 10 y 30 20 10 10 20 30 2 X 0 4 3 2 2 1 30 25 20 15 c Approximate any relative maximum or minimum values Round your answers to three decimal places relative maximum x y 10 5 30 25 10 20 15 5 A y 1 2 0 4 b Use the graph to find the open intervals on which the function is increasing and decreasing Enter your answers using interval notation The function is increasing on X

2 7 pts In a group of 100 sports car buyers 40 bought alarm systems 30 purchased chosen at random bought an alarm system what is the probability they also bought bucket seats and 20 purchased an alarin system and bucket seats If a car buyer bucket sents

9 If you have a financial goal of 20 000 after 6 years how much should you dep every 3 months starting now in an account that compounds quarterly at a rate A E 1 n 1 5 5 7 pts Use P 8pts

Write this ratio as a fraction in simplest form without any units 4 feet to 54 inches You can use the table below to help convert the units Length Weight Capacity Volume 1 foot 12 inches 1 yard 3 feet 1 pound 16 ounces 1 pint 2 cups 1 quart 2 pints 1 gallon 4 quarts 010

Determine the truth value for the following statement when p is false and q is true q p Choose the correct answer below A False OB True