Algebra Questions

Find the inverse of f x x 3 by thinking about the operations of the function and then reversing or undoing them Choose the correct answer below OA f x x 3 OB f x x 3 OC f x y 3 OD f x y 3

Factor the polynomial by grouping 9x 9x x 1 A x 1 9x 1 B C x 1 9x 1 x 1 9x 1 D x 1 9x 1

Find the indicated term for the binomial expression 7th term 8 3x y The 7th term is

In the sequence below what term is the number 73 5 9 13 n Type a whole number

The graph shown below approximates the number of children in a country who lived with only their grandparents in the years from 1991 through 2009 The number of children is a Function f of the year x Approximate the number of children living with only grandparents n 1991 That is find f 1991 Number of children in millions 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 91 93 95 97 99 01 03 05 07 09 Year The number of children living with only grandparents in 1991 is appro million Type an integer or a decimal T

Use the graph to find the following a f 2 b the domain c any x values for which f x 1 d the range VITAL I Pit anys UCIC BIG CUITCUL CIVICE UCIOW au cuessary answer box es to complete your choice O A y ly OB y lyz OC yl sys OD ylys O E The range is all real numbers i 4 S 7 This question 1 point s pos 3 4 64 B 10 1 More 10

Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros Find the other zero 4 3 1 4i 3 The other zero is

Determine the other factor for 2ax 4ay 3bx 6by if one of the factors is 2a 3b A B C x 4y x 2y x 2y D x 2y 2

Determine the GCF of 6x y 12xy 9x y A B C D 3r y 36xy 36x y 3xy

Factor the following quadratic expression 15x 35x A 7x 5x 6 B 5x 3x 7 C 3z 5x 1 Not factorable

Factor the polynomial by grouping 4a 7a 4a 7 A 7a 9 a 4 B C 4a 7 a 1 7a 9 a 5 D 4a 7 a 2

Use the graph to find the following a f 2 D the domain c any x values for which f x 1 d the range For what x value s is f x 1 Select the correct choice below and if necessary fill in the answer box to complete your choice A X Use a comma to separate answers as needed OB There is no value of x for which f x 1 What is the range Select the correct choice below and if necessary fill in the answer box es to complete your choice CO 10 k 7 10 8 8 4 2 6 10 O 0 10

Use the graph to find the following a f 2 b the domain c any x values for which f x 1 d the range f 2 What is the domain Select the correct choice below and if necessary fill in the answer box es to complete your choice OA x1xs OB x1 x OC x1x OD x1x E The domain is all real numbers 10 8 8 10 8 4 Ay

Consider the equation 4x 20 6x Without solving how do you know that x 2 is an extraneous solution BIUE T T

Determine whether the correspondence is a function Domain 4 3 6 Range 4 Is the correspondence a function O A Yes because each element in the range corresponds to exactly one element in the domain OB No because an element in the domain corresponds to more than one element in the range C No because an element in the range corresponds to more than one element in the domain OD Yes because each element in the domain corresponds to exactly one element in the range

10 28v 16v 21v 12 12 49x 35x 56x 4

9 96n 84n 112n 98 11 4v 12v 5v 15

2 12p 21p 28p 49 4 6v 16v 21v 56 6 214 844 154

Factor each completely 1 8r 647 r 8 3 12x 2x 30x 5 5 63n 54n 105n 90

The perimeter P in yards of a soccer field is represented by the formula P 21 2w where is the length in yards and w is the width in yards W 10 yd l 100 yd a Solve the formula for W b The perimeter of the soccer field is 330 yards Find the width of the field Width yards c About what percent of the field is inside the circle Round to the nearest tenth of a percent The percent of the field is C

A person purchased a used Chevrolet Cavalier for 4500 The car is expected to decrease in value by 22 each year over the next several years What would be the decay factor of a model that would represent the value of the car 0 78 0 990 0 22 1 22

ose g n 2n 1 h n 2n 3 Find goh n A B C D 3n 16 4n 7 4n 1 4n 1

Which equation would you use to find the amount of money you have if 700 is invested at an interest rate of 5 75 compounded monthly for 25 years Compound Interest Formula A P 1 n O A 700 1 A 0 0575 700 1 0 575 25 700 1 12 25 25 A 700 1 0 0575 0 0575 12 12 25

f x 2x 5 Find fog 3 fog 3 g x is as defined in the function below 9 8 7 6 5 3 2 1 9 8 7 6 5 4 3 2 1 N 2 3 45678 5 6 8 y 3 0 2 8

At Generic Middle School 8 students were sick with the flu on the first day of school By the end of the first week 12 students were sick and by the end of the 2nd week there were 18 students sick The attendance clerk noticed that the number of students getting sick was growing exponentially with a growth factor of 1 5 A function model that describes the number that have gotten sick would S x 8 1 5x where x is the number of weeks completed at school Using the model how many students could be expected to have been sick by the en of the 6th week approximately 41 students approximately 205 students O approximately 91 students approximately 72 students

f x x 5 g x is as described in the table below g x A 17 Find fog 9 B 25 C 95 C H 10 2 2 6 3 12 4 20 5 30 6 42 7 56 8 72 9 90 10 11

Simplify each expression b 5 2b 12b 16 1 A 3 b 5 2b b 4 7 2 b 9 24k 16k 3k 1 14b 20b 146 48b 40 6 b 5 b 3 B D b 3 b 1 b 4 27k 18k 27k 9k Find each product 5 7p 3 6p 1 A 16p 64p 64 B 42p 25p 3 C 16p 64p 64 2 4 6 2 40n 56n 35n 49 5n 38n 48 5n 8 4 8n 7 n 6 A B 70m n 9 n 5 C n 6 D 10n n 4 7m 4 49m 28 14m 28 12m 24 6 6k 1 7k 2 A 42k 19k 2 B 4k 16k 12 C 42k 2 5k 2

7 8k 8 k 5 A 8k 32k 40 B 8k2 48k 40 C 8k 48k 40 D 8k 40 9 2a 2 3a 5a 6 A 28a 63a 19a 20 B 6a 16a 22a 12 C 10a 27a 32a 14 D 56a 29a 8a 20 11 7n 1 n 2n 6 A 7n 53n 27n 24 B 7n 15n 44n 6 C 16n 58n 72n 18 D 32n 28n 22n 5 8 10 12 8 7x 1 5x 7 A 35x 54x 7 B 35x 7 C 35x 44x 7 D 35x 54x 7 10 8n 7 7n 5n 3 A 12n 46n 14n 42 B 8n 32n 8n 48 C 15n 17n 22n 24 D 56n 89n 59n 21 12 x 4 7x 8x 3 A 32x 68x 37x 6 B 7x 20x 35x 12 C 21x 52x 35x 4 D 49x 28x 40x 24

An airplane is flying with a constant altitude at a speed of 450 mph in a direction 10 north of west directly towards its final destination The airplane then encounters wind blowing at a steady 32 mph in a direction 75 north of east a Start by drawing a vector diagram for this situation Did you draw a diagram Yes Great Your diagram might look something like this i Speed 448 55 ii Direction 0 11 Wind b If the pilot does not correct his course after encountering the wind at what speed and in what direction counterclockwise from east will the plane be traveling 0 1116 mph New Path Original Path Preview Preview c If the airplane had encountered no wind at all it would have reached its final destination in two hours along its original course Assuming the pilot never corrected his course and that the wind continues to blow at the given speed and direction how far from its final destinations is the airplane after two hours of flying under the given conditions miles Preview 0 1116 0 1116 Truagain Look at the diagram in nart a If the wind blows at 32 mph for two hours how many miles will the wind move the plane

The size of a rat population at the bay area of a certain city grows at a rate of 7 monthly If there are 150 rats currently find how many rats rounded to the nearest whole should be expected in 12 months Use y 150 2 7 0 07t and let t be 12 months Y rats

Given the graph of the polynomial function write the function as g x in intercept form JA 2 4 2 X

Observe the graph and identify the following key features 1 Identify the intercepts 2 If n is odd or even 3 The number of turns 4 If constant a is positive or negative 5 The degree of the polynomial 17 JA 2 12345 1 2 5

Identify the transformations of the graph of f x x that produce the graph of the given function g x Then graph g x on the same coordinate plane as the graph of f x by applying the transformations to the reference points 1 1 0 0 and 1 1 g x x 2 Reference Points 1 1 0 0 1 1 First Transformation Second Transformation 4 2 4 2 0 2 2 4

Which graph is sketched to the right A g x x 1 x 2 x 3 B g x x 1 x 2 x 3 C g x x 1 x 2 x 3 2 0 X

Given the function y x 2 Place a point on the coordinate grid to show the x intercept of the function Place a point on the coordinate grid to show the y intercept of the function 8 6 4 2 8 6 4 2 2 P 6 2

Given the graph below determine whether each statement is true or false 19 W Ley Statement 3 is a zero of the function 0 is a zero of the function 1 is a zero of the function 2 is a zero of the function 4 is a zero of the function True False O

Which graph is sketched to the right A g x x 1 x 2 B g x x 1 x 2 C g x x 1 x 2 2 1 0

Which graph is sketched to the right A g x x 1 x 2 x 3 B g x x 1 x 2 x 3 C g x x 3 x 2 x 1

Given the function y x 1 Place a point on the coordinate grid to show the x intercept of the function Place a point on the coordinate grid to show the y intercept of the function 6 2 8 6 4 2 ty 0 2 2

Given the graph below determine whether each statement is true or false Statement 3 is a zero of the function 2 is a zero of the function 1 is a zero of the function 0 is a zero of the function 1 is a zero of the function True False 0000

Which graphs is sketched below 0 N A g x x x 3 B g x x x 3 C g x x x 3 D g x x x 3

The graph of f x x with three reference points is shown Which of the following represents points from f x to a point on g x 2 x 4 3 Select three that apply A 5 3 B 5 1 C 3 5 D 4 3 E 2 5 4 2 4 2 O 2 y 4 2 4 X

How is the graph of g x x 3 related to the graph of f x x A The graph of g x is a translation of the graph of f x right 3 units and a reflection across the y axis B The graph of g x is a translation of the graph of f x down 3 units and a reflection across the x axis C The graph of g x is a translation of the graph of f x right 3 units and a reflection across the x axis

How is the graph of g x 6x 2 related to the graph of f x x

How is the graph of g x x 1 related to the graph of f x x A The graph of g x is a translation of the graph of f x down 1 unit B The graph of g x is a translation of the graph of f x up 1 unit C The graph of g x is a translation of the graph of f x right 1 unit

How is the graph of g x 2x related to the graph of f x x

How is the graph of g x x 1 related to the graph of x x

5 Find the equation of a line that passes through 5 2 and 1 3 in a point slope form b slope int form c general form

Bear Grylls was dropped off in the wilderness and spots a camp 30 west of north He proceeds to hike 15 east of north for 2 5 miles and determines the camp is now 70 west of north How far is he from the camp at this point Answer to the nearest hundredth of a mile

Explain the errors in 3 of the 4 calculations below Then fix where possible 2 10 6 2x 10 10 1 2x 18 12 18 18 2x 6 2 2 x 3 3 12 10 4x 10 10 4 2x 2 2 2 X 4 12 4x 10