» Avery states that the graph of g is the same as the graph of f with every
point shifted vertically. Cindy states that the graph of g is the same as the
graph of f with every point shifted horizontally.
f(x)=2x+1
g(x)=2x+3
Give an argument to support Avery’s answer
Give an argument to support Cindy’s statement

Answers

Answer 1

Answer:

Avery is right, because [tex]g(x) = f(x)+2[/tex].

Cindy is right, because [tex]g(x) = f(x+1)[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] functions, then [tex]g(x)[/tex] is the vertical translated version of [tex]f(x)[/tex] if and only if:

[tex]g(x) = f(x)+k[/tex], [tex]\forall \,k\in \mathbb{R}[/tex]

[tex]k = g(x)-f(x)[/tex]

If we know that [tex]f(x) = 2\cdot x + 1[/tex] and [tex]g(x) = 2\cdot x + 3[/tex], then:

[tex]k = (2\cdot x + 3) - (2\cdot x +1)[/tex]

[tex]k = 2[/tex]

Then, Avery is right, because [tex]g(x) = f(x)+2[/tex].

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] functions, then [tex]g(x)[/tex] is the horizontal translated version of [tex]f(x)[/tex] if and only if:

[tex]g(x) = f(x+k)[/tex], [tex]\forall \,k\in \mathbb{R}[/tex]

If we know that  [tex]f(x) = 2\cdot x + 1[/tex] and [tex]g(x) = 2\cdot x + 3[/tex], then:

[tex]g(x) = 2\cdot x + 3[/tex]

[tex]g(x) = 2\cdot x + 2 + 1[/tex]

[tex]g(x) = 2\cdot (x+1)+1[/tex]

[tex]g(x) = f(x+1)[/tex]

Then, Cindy is right, because [tex]g(x) = f(x+1)[/tex].


Related Questions

Simplify to create an equivalent expression. 617 - 3y) + 6(y + 1)​

Answers

You have to simplify

Answer:

623+3y

Step-by-step explanation:

You distribute the 6 then you add the ys and the numbers together

Multiply. Answer with a mixed number in simplest form

2 1/5 x 3 4/7

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Answer:

7.85714285714

Explanation:

hrnvkdkdjcnvnskdkxjcnfkdldjgnvnfkdk

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Answer:

32 minutes and 30 seconds.

Step-by-step explanation:

3 hours = 180 minutes, plus 15 added = 195 so 195 ÷ 6 = 32.5 or 32 mins and 30 seconds

Answer:

32.5 minutes

Step-by-step explanation

60x4-45/6

what is the simplified form of the fraction 7/28

Answers

Answer:

1/4

Step-by-step explanation:

7 divided by 24 = 4 so it gets reduced to 1 and then 1/4

The solution is: 1/4  is the simplified form of the fraction 7/28.

Here, we have,

given that,

the fraction is: 7/28

now, we divide each fraction numerator and denominator by a common divisor of them,

here, we know that,

7 * 1 = 7

7*4 = 28

so, the gcf of 7 and 28 = 7

we divide each fraction numerator and denominator by a common divisor 7,

we will get:

7/28 = 1/4

7 divided by 28 = 4 so it gets reduced to 1 and then 1/4.

Hence, The solution is: 1/4  is the simplified form of the fraction 7/28.

To learn more on fraction click:

brainly.com/question/10354322

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Denis orders a large pizza for $16.50 plus $2 for each topping. Sheng orders a medium pizza for $13.25 plus $2 for each topping.

Answers

Their bills will never be the same because the toppings cost the same.

Question must probably wants to know the number of toppings it would take for their bills to be equal.

Assume the number of toppings is x, Dennis's bill will be:

= Cost of Pizza + Cost of toppings x number of toppings

= 16.50 + 2x

Sheng's bill will be:

= 13.25 + 2x

Equate their bills to find the number of toppings that would equate their costs:

16.50 + 2x = 13.25 + 2x

16.50 - 13.25 ≠ 2x - 2x

3.25 ≠ 0

In conclusion, their bill will never be the same because the toppings are the same price.

Find out more at https://brainly.com/question/5607279.

(03.01 LC)

The leg of a right triangle is 3 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle? (1 point)

Question 1 options:

1) The square root of 5
2) The square root of 7
3) 5
4) 7
Question 2 (1 point)
Saved
(03.01 LC)

What is the length of the hypotenuse of a right triangle if each of the two legs is 7 units? (1 point)

Question 2 options:

1) Square root of 14

2) 7

3) The square root of 98

4) 49

Answers

Answer:

√7 units, √98 units

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2. So 9+b^2=16. So b^2=7. So b=√7

a^2+b^2=c^2. SO 49+49=c^2. So 98=c^2. So c=√98.

Answer:

√7 units, √98 units

Step-by-step explanation:

all poets are loners. All loners are taxi drivers. therefore, all poets are taxi drivers

is this valid or invalid?

Answers

Answer:valid

Step-by-step explanation:

Graph a scatter plot using the given data.

Answers

Answer:

Here is the answer.

Step-by-step explanation:

Pls help me out I give u a cookie

Answers

Answer:

C. Division property of equality

Step-by-step explanation:

Both sides of the equal sign are divided by 10, which clearly means that the division property should be applied here.

Answer:

divison property of equality is the reason

hope it helps you

Each angle of the equilateral triangle in the figure has measure (2x – 9)°. Determine the value of x.

A) x = 25.5
B) x = 34.5
C) x = 69
D) x = 60

Answers

Answer:

34.5

Step-by-step explanation:

An easy way to find this out is plug in all the answers into our equation until we get 180. So here's what you do:

A) X=25.5

So put that in the equation replacing x like this :  2(25.5)-9 =42 then multiply by three which = 126, So, A) is not our answer, now do it with the rest until you get 180,

2(34.5)-9=60 60x3=180 so your answer will be the number you plug in aka:34.5

Hope this helps you understand the topic a little better <3

Can someone help me!

Honeydew melons are on sale at four different grocery stores. Which store
offers the lowest unit rate for honeydew melons, in dollars per pound?
$3.50
Happy Grocery:
7 pounds
.
sto
• Sullivan's:
5 pound
• Mother Nature:
$4.00
10 pounds
• Farmer's Pride: $0.45/pound

Answers

Answer:

Mother Nature

Step-by-step explanation:

Do you want one? Prolly will waste my time sorry :(

Answer:I would think c but let me check

Step-by-step explanation:

(Please help!!) Arnold is paid a graduated commission on sales. He earns 7% on sales up to $10,000 and 10% on sales over that amount. His goal is to make $2,500 next month. How much will he need to sell?

Answers

Answer:

Step-by-step explanation:

10000*7%= $700.00

2500-700=1800

1800 is 10% of 18,000

So 18,000 +10,000 = 28,000 in sales is needed to get $2,500 in commission.

A new car is purchased for 24600 dollars. The value of the car depreciates at 5.5% per year. To the nearest year, how long will it be until the value of the car is 11300 dollars?

Answers

Answer:

The number of years until the value of the car is 11300 dollars is 9 years.

Step-by-step explanation:

This can be calculated using the following formula:

Value of the Car = Purchase cost - (Annual depreciation expenses * N) ........ (1)

Where;

N = Number of years until the value of the car is 11300 dollars

Purchase cost = $24,600

Annual depreciation rate = 5.5%

Annual depreciation expenses = $24,600 * 5.5% = $1,353

Value of the car = $11,300

Substituting the value into equation (1) and solve for N, we have:

$11,300 = $24,000 - ($1,353 * N)

$1,353 * N = $24,000 - $11,300

$1,353 * N = $12,700

N = $12,700 / $1,353

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N = 9

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Answer:

14

Step-by-step explanation:

A triangle is translated by using the rule (X.Y) =(x-4.y+1). Which describes how the figure is moved?
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Answers

four units left and one unit up

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(1, 3)
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Answers

Answer:

(1,3)

Step-by-step explanation:

im pretty sure its (1,3)

Help Really quick
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Answer:

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Step-by-step explanation:

Answer:

3 and 2/3b + 1a

Step-by-step explanation:

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Answers

Answer:

No

Step-by-step explanation:

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Answers

Answer:

It's 27

Step-by-step explanation:

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Answers

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2
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Answers

Answer:

x = 2

Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

74 is the answer !!!!

Starting from the same place a plane took 1 hr longer to fly 705 mi to Atlanta, than to fly 470 mi to New Orleans. If the plane flew at the same rate for the entire trip, what was the flying time for the shorter leg? a. 1 2 hr c. 1 1 2 hrs b. 1hr d. 2 hrs

Answers

Answer: d. 2 hrs

Step-by-step explanation:

Let x = Time taken(in hours) to fly 470 mi to New Orleans. (Shorter leg)

Then Time taken to fly 705 mi to Atlanta= x+1 (longer leg)

Since  the plane flew at the same rate for the entire trip.

i.e. Speed 705 mi to Atlanta = Speed to fly to New orleans

[tex]\Rightarrow\ \dfrac{705}{x+1}=\dfrac{470}{x}\ \ \ \ \ \ \ [\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}]\\\\\Rightarrow\ 705x=470(x+1)\\\\\Rightarrow\ 705x=470x+470\\\\\Rightarrow\ 705x-470x=470 \\\\\Rightarrow\ 235x=470\\\\\Rightarrow\ x=\dfrac{470}{235} \\\\\Rightarrow\ x=2[/tex]

hence, the flying time for the shorter leg = 2 hours

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ty and his 3 brothers share a pizza equally what is the fraction

Answers

Answer:

If they all get an equal slice, 1/4.

Step-by-step explanation:

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Answer:

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The question is Find the constant of proportionality in the graph below

Answers

Answer:

4.5

Step-by-step explanation:

What is the equation of a line that has a slope of 2/5 and passes through the
point (-5,5)? *

Answers

Answer:

y = 2/5x + 7

Step-by-step explanation:

substitute 2/5 in for m and (-5,5) in for (x,y) respectively to find the y intercept

y=mx+b

5 = 2/5(-5) + b

5 = -2 + b

add 2 to both sides to solve for b (y intercept)

b = 7

therefore the equation for the line will be...

y = 2/5x + 7

SI Unit is used for scientific work why?​

Answers

Answer:

SI is used in most places around the world, so our use of it allows scientists from disparate regions to use a single standard in communicating scientific data without vocabulary confusion.

7. The graph of a polynomial function is shown.

a. Is the degree of the polynomial odd or even? Explain how you know.

b. What is the constant term of the polynomial?

Answers

9514 1404 393

Answer:

even-4

Step-by-step explanation:

When the end behavior is the same sign on the left and the right, the degree is even. This polynomial is of even degree.

The y-intercept is the constant term: -4. (All the other terms are zero when x=0.)

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