Functions Questions and Answers

Write an equation of the form y a sinbx or y a cos bx to describe the graph below AN sino cos

Write the transformed function of x if a y x if a 3 b 2 h 5 and k 1

Entity theorists generally adopt goals incremental theorists generally adopt goals O performance performance O learning learning O performance learning

Graph the function on the interval 6 6 h x int 5

Simplify the trigonometric expression

Which word from the following list matches part C of the division dividend divisor quotient remainder 29 A D 8 235 B 16 75 The word that matches with part C of the division is 72 3

A rain gutter is to be installed around a house whose foundation is shown to the right Find the perimeter of the house then find the total cost of the gutter The gutter costs 3 42 per ft The perimeter is 83 ft 23 ft 89 ft 27 ft

Identify the number as rational or irrational If the number is rational find the root exactly If the number is irrational approximate the number to the nearest thousandth 14 Is 14 rational or irrational O Rational O Irrational www

Find the area of a rectangle 68 8 cm by 18 3 cm The area of the rectangle is Type a whole number or a decimal Round to the po

Which of the following is NOT a requirement of the Combinations Rule Cr n rl n r for items that are all different Choose the correct answer below OA That there be n different items available OB That order is taken into account consider rearrangements of the same items to be different sequences OC That order is not taken into account consider rearrangements of the same items to be the same OD That r of the n items are selected without replacement

The domain of discourse consists of all positive intergers Z What are the truth values for each of the following i Vzy r y ii Vzy x y 0 iii 3zVy r y iv 3z3y ry 0

2 Which of the following functions are one to one Select all that apply Of2 Z Zwith f2 x x4 Of3 RR with f3 x e Ofi Z Zwith fi x x Ofa R Zwith f x

Find the Wronskian for the set of functions x sin x cos x

n Decide if x y R 1 y 2 is a function b Given R R f x 4 i check if f is a function and find R ii find f 1 5 f 2 3 2 1 1 4 c Sketch on separate sets of axes X 1 5 and X 2 4 and therefore X 15 X 24 2 2 4

Using the equation 1 x 2 5 X Find the missing value for y on the following table of values Round your answer to the nearest hundredth X 0 10 4 10 31 y 4 11 Your Answer

As blood moves through a vein or artery its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases see the figure below For an artery with rac 0 7 cm v in cm s is given as a function of r in cm by v g r 18 500 0 49 a Find g What does g represent 1 09 represents the velocity of the blood in the vein or artery at time t 1 g represents the velocity of the blood in the vein or artery with radius r o g represents the length of the vein or artery that contains blood with velocity v Og represents the radial distance from the center of the vein or artery that contains blood with velocity v Og g represents the amount of blood passing through the vein or artery in time t 1 b Find g 45 Round your answer to three decimal places g 45 What does your answer represent It represents the velocity of the blood in the vein or artery at time 45 s It represents the velocity of the blood in the vein or artery with radius 45 cm It represents the length of the vein or artery that contains blood with velocity 45 cm s It represents the radial distance from the center of the vein or artery that contains blood with velocity 45 cm s

If g x x 10x with x 2 5 find g 11

Determine whether the function is one to one f x x 9 0 x 7 is one to one is not one to one

a The average rate of change of a function f between x a and x b is the slope of the Select line between a f a and b f b b The average rate of change of the linear function f x 7x 2 between any two points is

The graphs of the functions and g are shown The function has a greater average rate of change between x 0 and x 1 The function has a greater average rate of chang x 1 and x 2 The functions fand g have the same average rate of change between x and x 9

From the graphs of f and g in the figure we find the following Assume that each point lies on the gridlines f g 1 f g 1 fg 1 4 0

By definition fog x So if g 1 5 and f 5 25 then fog 1

Express the function F in the form fog Enter your answers as a comma separated list Use non identity functions for f x and g x F x x 8 8 f x g x

Let f and g be functions a The function f g x is defined for all values of x that are in the domain s of Select b The function fg x is defined for all values of x that are in the domain s of Select c The function f g x is defined for all values of x that are in the domain s of Select B and g x is not equal to

Let f and g be functions The composition fog x is defined for all values of x for which x is in the domain of Select and g x is in the domain of Selec

Consider the following functions f x x1 g x 8x 10 Find fog x Find the domain of fog x Enter your answer using interval notation Find gof x Find the domain of gof x Enter your answer using interval notation Find f of x Find the domain of f of x Enter your answer using interval notation Find gog x

Find f g f g fg and f g and their domains f x 25 x g x x 2 Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find X Find the domain of Enter your answer using interval notation

Find the domain of the function Enter your answer using interval notation x 3 X 6 k x

For the following function f x 4x 11x 20 a Find the values of x for which f x 0 b Find f 0 Express numbers using Integers or simplified fractions Part 0 2 Part 1 of 2 Separate multiple answers using a comma if necessary f x 0 when x 0 0 X 8 5

the feedback in case you need to make any corrections Please make sure to include your work handwritten is preferable Graph the system of linear inequalities BY HAND Show the solution region Pay close attention to dashed solid lines and shading above below when graphing each inequality y 4x 2 x21 1 y S 10 8 6 4 2 y x 4 x 2y 6 10 1980 2 2 526 2 10 6 1226 4 2 2 4 6 8 10 Algebraically 2 5 54 2 4 521 4 545 4 false 6 8 10 2 y x This is true but since 2 5 does not satisfy it is Ihot a selution to the 10 8 6 4 10 2 57 8 o 6 5 4 2 3 Determine if 2 5 and 4 2 are solutions to the system of inequalities both algebraically and graphically Show your work algebraically Graphically draw and shade both inequalities Then plot each ordered pair to confirm the answers you found algebraically 15 2 4 6 8 10 2 4 Graphically Algebraically 4 2 4 2 226 4 4 6 836 This is true so 4 2 satisfies both inequalites 10 86 and is a solution to the systern 6 8 10 10 4 2 8 6 44 2 2 4 6000 4 6 8 10 2 4 6 8 10

A polynomial f x and one or more of its zeros are give f x 14 19 3 101 226 04 712

A polynomial f x and one or more of its zeros are given f x x 18x 104x 36x 212 LE

Write a polynomial f x that satisfies the given conditions 9 Degree 3 polynomial with Integer coefficients with zeros 9i and 5 f x X 3

N f x 1 n Evaluate the function f x x 3x for the given value of x f x 1

Review for Test 2 Sections 1 6 to 2 4 Question 3 of 29 1 point I Question Attempt 1 of Unlimited The graph of y f x is given Graph the function y f x 2 3 8 6 9 8 7 6 5 4 3 2 1 3 y f x O 2 3 4 5 6 7 4

Write the equation of a sine or cosine function to describe the graph AA 2 TE IM 4 3 5 3 7 T 0 0 Es X

The function h x f 3x 4 is created from transformations of the function f x

Fill in the information about the absolute value functions below a For each function choose whether its graph opens upward or downward b Choose the equation with the narrowest graph c Choose the equation with the widest graph y 2 x Choose one O y Choose one 0 y 3 x Choose one y 4 Choose o

Simplify the expression This type of expression arises in calculus when using the quotient rule 6 2 x 3 x 2 x 2 3

y x 51 X 3 2 1 0 1 2 3 Sketch the graph of the equation 10 y in 10 5 S y 10 y 10 5 10 X 10 5 10 16 5 10 y y 10 5 10

Find all real solutions of the equation Enter your answers as a comma separated list If there is no real solution enter NO REAL SOLUTION 3x 3 1 x 2 X

Simplify the expression This type of expression arises in calculus when using the quotient rule 3x x 6 x 6 x 6 x 6

1 2 Solve the equation 2z 3z 27 0 The solution set is 3 4 3

E Question 23 of 28 1 point I Question Attempt 1 of Unlimited Refer to functions m and q Evaluate q m x and write the domain in interval notation Write your answers as Integers or simplified fractions m x x 3 1 x 8 Part 0 2 Part 1 of 2 q x 8 X S

Not yet answered Marked out of 2 00 The general solution of the following second order linear ODE y 3y 2y 0 is O a y x C e c e 2x O b None O c y x c e c e O d y x c e Oe y x c e c e

2 00 The function y x e is the solution of the following IVP y y y 1 1 O True O False

Not yet answered Marked out of 2 00 One of the following is a solution of the differntial equation y xy 0 Qa None O b O C O d 2 e 2 1 LIT e 2 Oe x

where Describe UA and A where A is the collection of sets of the form An Civen the relation r CZ such that me 2 n n TEM

The graph of a x is shown below let b x 2 x 2 3 Graph 4 x and b x on the same Set of axes a x n 5 5

if x 4 cx Let f x 10 dx if x 4 Find c d so that f x is continuous for all x d C