Describe each graph in relation to its basic function.
a. Compare f(x) = (x - 2)^3 - 1 to the basic function g(x) = x^3
Explain in full sentences please!

Answers

Answer 1

Answer:

In a nutshell, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation.

Step-by-step explanation:

Let be [tex]g(x) = x^{3}[/tex] the parent function, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation, that is:

[tex]f(x) = g(x-a)-b,\,a,b\in\mathbb{R}[/tex] (1)

If [tex]a > 0[/tex], then translation is rightwards.

If [tex]b > 0[/tex], then translation in downwars.

If [tex]a = 2[/tex] and [tex]b = 1[/tex], then the resulting function is:

[tex]f(x) = g(x-2)-1[/tex]

[tex]f(x) = (x-2)^{3}-1[/tex] (2)

In a nutshell, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation.


Related Questions










Find the sum or difference. Write your answer in simplest form

3/8 + 1/4​

Answers

Answer:

5/8

Step-by-step explanation:

5/8 which is in simplest form

Answer:

5/8

Step-by-step explanation:

3/8+1/4 = 3/8+2/8 = 5/8

Y- 4/9 = 2 2/3


Y= ?

What is y = ?

Answers

Answer: X= 3 1/9


Step by step:

X-4/9=2 2/3

2 2-3+4/9=

=2 6/9+4/9=

=3 1/9

How do scientists identify tectonically active regions

Answers

Answer: plate tectonics

Step-by-step explanation:Most earthquakes and volcanic eruptions do not strike randomly but occur in specific areas, such as along plate boundaries. One such area is the circum-Pacific Ring of Fire, where the Pacific Plate meets many surrounding plates. The Ring of Fire is the most seismically and volcanically active zone in the world.

Earthquakes

Sina Au,Jho at Tess ay anak ng mag asawang sing ng
Roy at Aling Lita, Si Ay ay 7 taon na mas matanda kay the
at 2 taon mas bata kay Tess, Kung ang kabuyang edad ay
70. llan taon si Au?​

Answers

Answer: Sina Au,Jho at Tess ay anak ng mag asawang sing ng

Roy at Aling Lita, Si Ay ay 7 taon na mas matanda kay the

at 2 taon mas bata kay Tess, Kung ang kabuyang edad ay

70. llan taon si Au?​

Step-by-step explanation:

Do y'all play warlock, hunter, or titan?

Answers

Answer:

I would probably choose warlock if my computer could handle it ;w;

Please help me with an explanation so i can understand it better

Answers

Answer:

9.5

Step-by-step explanation:divide area by 12.3

i think it is right

Answer:

u= 19 miles

Step-by-step explanation:

Area of triangle= ½ ×base ×height

Given that the area is 116.85 mi² and height= 12.3 mi,

116.85= ½ ×u ×12.3

6.15u= 116.85

u= 116.85 ÷6.15 (÷6.15 on both sides)

u= 19 mi

Two similar polygons are shown below.
Which transformation was performed on PORS to form POR'S?
O A dilation factor of 2
O A dilation factor of 4
O A dilation factor of
07 1 / 을
A dilation factor of

Answers

Answer:

??

Step-by-step explanation:

을("eul") ?????

Jaleah needs some string to make bracelets. She needs
enough string to make 32 bracelets. Each bracelet takes 9 3/4
inches of string. How much string will Jaleah need to make
the bracelets?

Answers

Answer:

312

Step-by-step explanation:

3/4 × 32 = 24

9 × 32 = 288

288 +24=312

Lee el siguiente planteamiento y resuelve los problemas:

Un globo electrostáticamente cargado ejerce una fuerza de atracción sobre un papel de tal forma que se pueden identificar dos cargas positivas en la periferia del globo y una negativa en la periferia del papel. Las cargas del globo y del papel están colocadas en los vértices de un triángulo equilátero cuyos lados tienen una longitud de 5 cm, tal como se muestra en la figura. Se sabe que la carga q1 tiene polaridad negativa con un valor de 20 μC (microcoulomb), la carga q2 tiene polaridad positiva con una magnitud de 10 μC y la carga q3 también tiene polaridad positiva con una intensidad de 30 μC.


Calcula la fuerza de q3 sobre q1. Para ello, hay que sustituir los valores de las respectivas cargas en la ecuación de la ley de Coulomb y el valor de la distancia d , la cual corresponde a la separación entre q1 y q3.

Realiza el cálculo de la fuerza de q2 sobre q1.

a. Utiliza el plano cartesiano para graficar los resultados de las fuerzas solicitadas.

Determina la magnitud de la fuerza de atracción resultante que ejercen las cargas q2 y q3 sobre q1 y el ángulo del vector de la resultante.

a. Utiliza el plano cartesiano para graficar el resultado, de la magnitud de la fuerza de atracción.

Answers

Answer:

I am read well any things please I don't know how to run this app please helpe I don't need this app by saying this much i want to stop my points

thanks

The speed of the current in a creek is 5 mph. A person clan kayak 3 mi upstream in the same time that it takes him to kayak 13 mi downstream. What is the speed
the person's kayak in still water?
The speed of the person's kayak in still water is

Answers

Answer:

8

Step-by-step explanation:

0) the basic formula is: L=v*t, where L - distance, v - speed/velocity; t - time;

1) if the person's speed in still water is 'v' and the speed of water is 5 (according to the condition), then the upstream speed is 'v-5' and the downstream speed is 'v+5';

2) according to the condition the upstream time and the downstream time are the same, it means t₁=t₂=t, where t₁=upstream time and t₂=downstream time;

3) according to the items above it is possible to make up the equation of the upstream travel: t(v-5)=3; ⇒ t=3/(v-5);

4) according to the items above it is possible to make up the equation of the downstream travel: t(v+5)=13; ⇒ t=13/(v+5);

5) if t=3/(v-5) and t=13/(v+5), then

[tex]\frac{3}{v-5} =\frac{13}{v+5}; \ => \ v=8.[/tex]

Which of the following equations is the result after the first step in solving 5x – 4 = 15? A. x – 4 = 3 B. x = 2 C. 5x = 19 D. 5x = 11

Answers

Answer:

C

Step-by-step explanation:

5x-4=15

5x=15+4

5x=19

City Hall is planning to construct a new building. The height of each triangular-shaped face on the top of the building will be 75 feet. The diagram shows all the building dimensions.

Calculate the total area of the exterior faces of the building (do not include the base area). Show your work.

Answers

Answer:

74 630 ft

Step-by-step explanation:

85×182×4+1/2×85×75×4

pls help with both the equations​

Answers

Answer:

what is the question send it in the comment fast

III. Fill in the gaps with the correct form of the verbs in brackets.
(go) early
1. If you
(not/want) to stay in the party, we
2. You
(pass) your exams if you
(study) really hard.​

Answers

Answer:

give us a more zoomed out picture

Step-by-step explanation:

Can’t be bothered to do the rest so I need the answers

Answers

Answer:

25.=0.06

26.=0.03

27.=0.12

28.=0.21

29.=0.21

30.=0.31

31.=0.34

32.=0.16

33=0.34

34.=0.04

35.=0.06

36.=0.15

37.=0.24

38.=0.36

39.=0.25

40=0.09

41=0.35

42=0.14

43=0.15

44=0.24

45=0.53

46=0.42

47=0.31

48=0.35

49=0.35

50=0.24

51=0.54

52=0.05

53=0.24

54=0.68

55=0.19

56=0.51

57=0.66

58=0.43

59=

60=

Am missing some don't got time to go over

Step-by-step explanation:

Russell wants to buy three ties and a belt and must spend no more than $80.00. The belt costs $28.50. If the three ties are the same price, then how much can he pay for each tie

Answers

Answer: $17.16

Explanation: do you have to start by subtracting the cost of the belt from the total budget: 80-28.5= 51.5. Then you can divide the remaining money by three because he’s buying three ties: 51.5/3≈ $17.16

Answer:$17.16

Step-by-step explanation:

do you have to start by subtracting the cost of the belt from the total budget: 80-28.5= 51.5. Then you can divide the remaining money by three because he’s buying three ties: 51.5/3≈ $17.16

What is the multiplicative inverse of y?

Answers

Answer:

The multiplicative inverse of y is [tex]\frac{1}{y}[/tex].

Step-by-step explanation:

Multiplicative inverse implies a value that you would multiply with the given value so as to give 1.

Let the multiplicative inverse of y be represented by a, so that;

a x y = 1

ay = 1

divide both sides by y to have,

a = [tex]\frac{1}{y}[/tex]

Thus, the multiplicative inverse of y is [tex]\frac{1}{y}[/tex].

This is applicable to any given value. Examples:

i. Given 2, the multiplicative inverse is [tex]\frac{1}{2}[/tex].

⇒ 2 x [tex]\frac{1}{2}[/tex] = 1

ii. What is the multiplicative inverse of 5?

The required answer is [tex]\frac{1}{5}[/tex].

Levin Furniture buys a living room set with a $4,900 list price and a 50% trade discount. Freight (FOB shipping point) of $45 is not part of the list price. What is the delivered price (including freight) of the living room set, assuming a cash discount of 4/10, n/30, ROG? The invoice had an April 8 date. Levin received the goods on April 19 and paid the invoice on April 25.

Answers

Delivered price =   $Answer:

Answer:Delivered price=$1,814

Step-by-step explanation

Explanation:

List Price = $4,000

Trade  discount = 55%

Price after discount = $4,000 - 55% x $4000

$4000- $2,200 =  $1,800

if Levin pays within 10 days he will have a discount of 2 %, which he did

Therefore 2% x $1800 = $36

Delivered price =   $1800 -$36+ freight charges ( shipping)

$1800 -$36 + $50=$1814

plss answer Part A #1 abc . i will give brainliest. late answers accepted​

Answers

Answer:

a. (3x² - 2x - 5) units²

b. (x² - x) units²

c. (2x² - x - 5) units²

Step-by-step explanation:

a. Area of the frame = L*W

L = (x + 1) units

W = (3x - 5) units

Area of the frame = (x + 1)(3x - 5)

Apply distributive property

x(3x - 5) +1(3x - 5)

3x² - 5x + 3x - 5

Area of the frame = (3x² - 2x - 5) units²

b. Area of the picture = L*W

L = x units

W = (x - 1) units

Area of the picture = x(x - 1)

Apply distributive property

= x² - x

Area of picture = (x² - x) units²

c. Area of the frame that surrounds the picture = area of frame - area of picture

= (3x² - 2x - 5) - (x² - x)

= 3x² - 2x - 5 - x² + x (distributive property)

Add like terms

= 3x² - x² - 2x + x - 5

= 2x² - x - 5

Area of the frame that surrounds the picture = (2x² - x - 5) units²

PLEASE ANSWER THESE QUESTIONS CAREFULLY thank you so much

Answers

Answer:

Positive slope- line B

negative y-intercept- line C

slope of 0- line C

Step-by-step explanation:

Positive slope- line B This is because the line is angled upward on the right side

negative y-intercept- line C- the line is below the (0,0) mark

slope of 0- line C This is because the line isn’t angle upward nor downward.

Luis is shopping for gifts. Mugs are on sale for $4 off the regular price,p. Luis vuys 6 muga. H epays $54. What is the regular price of the mug? Show your work.​

Answers

Answer:

13

Step-by-step explanation:

Divide the total amount he paid by the amount of mugs he bought to find out how much each mug cost.

54 ÷ 6 = $9

Each mug is nine dollars, INCLUDING THE SALE which is $4 off.

Add $4 to $9 to find the regular price

$4 + $9 = 13

The regular price of the mugs based on the given equation will be $13.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation.

Suppose the regular price is x.

Selling price = $4 off of x = x - 4

Number of mugs buys = 6

Paid = $54

54= 6 (x - 4)

(x - 4) = 9

x = 13

Hence "The regular price of the mugs based on the given equation will be $13".

For more about the equation,

brainly.com/question/10413253

#SPJ2

Apply the distributive property to create an equivalent expression. 6(3c-5d+6) = ?​

Answers

Answer:

18c-30d+36

Step-by-step explanation:

6(3c-5d+6)

= 6(3c)-6(5d)+6(6)

= 18c-30d+36

A fruit stand sells bags of apples and tangerines. • Each bag has 3 fewer apples than tangerines. 2 • In each bag, the number of apples is the number of tangerines. Let A represent the number of apples in each bag and T represent the number of tangerines in each bag. Which system of equations can be used to solve for A and T?​

Answers

Answer: The system we need to use is:

A = T - 3

A = (2/3)*T

Solving this, we get:

In a bag, there are 9 tangerines and 6 apples.

Step-by-step explanation:

The question seems to be incomplete, by a quick online search i've found the complete question:

"A fruit stand sells bags of apples and tangerines. • Each bag has 3 fewer apples than tangerines. 2 • In each bag, the number of apples is 2/3 the number of tangerines..."

We know that:

A = number of apples in one bag

T = number of tangerines in one bag

We also know that:

"Each bag has 3 fewer apples than tangerines"

This can be written as:

A = T - 3

"In each bag, the number of apples is 2/3 the number of tangerines"

This can be written as:

A = (2/3)*T

Then we have a system of equations:

A = T - 3

A = (2/3)*T

This is the system of equations that can be used to solve for A and T, now let's solve this.

Because A means the same thing in both equations, then we can write:

A = T - 3 = A = (2/3)*T

Then:

T - 3 = (2/3)*T

We can solve this for T.

T - 3 = (2/3)*T

T - (2/3)*T = 3

(1 - 2/3)*T = 3

(1/3)*T = 3

T = 3/(1/3) = 3*3 = 9

This means that in each bag we have 9 tangerines in a bag.

Now we can use any of the two equations in the system to find the value of A.

I will use the first one:

A = T - 3

Now let's replace T by 9, then:

A = 9 - 3 = 6

A = 6

So there are 6 apples in a bag.

can you please help me with this question?​

Answers

Answer: 32, 25, and 13 are possible side lengths.

Step-by-step explanation:

The lengths of any two sides of a triangle must sum up to more than the length of the third side.

15 + 27 = 42

42 = 42

The sum has to be MORE than the third side.

15 + 27 = 42

42 > 11

15 + 11 = 26

26 < 27

The sum of two sides can't be LESS than the third side.

15 + 27 = 42

42 > 32

15 + 32 = 47

47 > 27

27 + 32 = 59

59 > 15

Possible Side Length!

15 + 27 = 42

42 < 45

Can't be less

15 + 27 = 42

42 > 25

15 + 25 = 40

40 > 27

27 + 25 = 52

52 > 15

Possible Side Length!

15 + 27 = 42

42 > 13

15 + 13 = 28

28 > 27

27 + 13 = 40

40 > 15

Possible Side Length!

Yup that is right I look it up

A line that includes the point (7,0) has a slope of 1. What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:y=x+0

Step-by-step explanation:

Help plz....................

Answers

Opposite sides in a parallelogram are equal
So,
XY=WZ
3a-4=a+2
2a=6
a=3

XW=YZ
b+1=2b
b=1

Expressions can be written using a combination of numbers and letters. Those values can also be described using words. Choose ALL expressions that are correctly described in words.

which is it

Answers

Answer:

A: 3a + 9: the sum of three times a and nine

C:15b − 10: ten less than the product of fifteen and b

Step-by-step explanation:

I just answer this question in US, and I got C right but choose the wrong answer for A.

These are the right answers.

A company is considering introducing two new products. Based on sampling results, the company is expecting a probability of success for Product A of 60% and a probability of success for Product B of 80%. The success of Product A is independent of Product B's success. What is the probability that both Product A and Product B will be successful

Answers

Answer:

I think b

-gxtpuf6a4t sketch see ura5wfyzrud

This is not a multiple choice, I need your help!

Answers

Answer:

Trapezoid, E, is the correct answer.

How many times does the line y=-6 intersect with the circle x^2+y^2=36?

Answers

Answer:

a) The line intersects with the circle once.

b) Tangent

Step-by-step explanation:

We are given the following equation for the circle:

[tex]x^2 + y^2 = 36[/tex]

How many times does the line y=-6 intersect with the circle?

We have to find the values of x when [tex]y = -6[/tex]

So

[tex]x^2 + y^2 = 36[/tex]

[tex]x^2 + (-6)^2 = 36[/tex]

[tex]x^2 + 36 = 36[/tex]

[tex]x^2 = 0[/tex]

[tex]x = 0[/tex]

Since the line intersects the circle at one point, it is tangent to the circle.

The line intersects with the circle once.

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