Ask question

Ask question

All categories

2 years ago

13

What is the equation of the graph

"absmiddle" class="latex-formula"> under a vertical stretch by the factor 2 followed by a horizontal translation 3 units to the left and then a vertical translation 4 units down?
a.) $y=2(x+3)^3+4$
b.) $y=2(x-3)^3+4$
c.) $y=2(x+3)^3-4$
d.) $y=2(x-3)^3-4$

1 answer:

Galina-37 [17]2 years ago

8 0

Answer:

C. y = 2 (x + 3)³ − 4

Step-by-step explanation:

y = x³

Stretch vertically by 2.

y = 2x³

Shift horizontally 3 units to the left.

y = 2 (x + 3)³

Shift vertically 4 units down.

y = 2 (x + 3)³ − 4

You might be interested in

A marine aquarium has a small tank and a large tank, each containing only red and blue fish. In each tank, the ratio of red fish

Anna007 [38]

Answer:

Ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

Step-by-step explanation:

Let the number of red fish and blue fish in the large tank are x and y respectively.

Similarly ratio of red fish and blue fish in the small tank are x' and y' respectively.

Since in each tank ratio of the red fish to blue fish is 333 : 444

That means x : y = 333 : 444

Or $\frac{x}{y}=\frac{333}{444}$

⇒ $\frac{x}{y}=\frac{3}{4}$

⇒ y = $\frac{4x}{3}$ --------(1)

Similarly x' : y' = 333 : 444

⇒ $\frac{x'}{y'}=\frac{333}{444}$

⇒ $\frac{x'}{y'}=\frac{3}{4}$

⇒ x' = $\frac{3y'}{4}$ ------(2)

Ratio of the fish in large tank to the fish in small tank is 464646 : 555

So (x + y) : (x' + y') = 464646 : 555

$\frac{x+y}{x'+y'}=\frac{464646}{555}$

Now we replace the values of x and y' from equation (1) and equation (2)

$\frac{(x+\frac{4x}{3})}{(\frac{3y'}{4}+y')}=\frac{464646}{555}$

$\frac{\frac{7x}{3}}{\frac{7y'}{4}}=\frac{464646}{555}$

$\frac{4}{3}\times \frac{x}{y'}=\frac{464646}{555}$

$\frac{x}{y'}=\frac{3}{4}\times \frac{464646}{555}$

$\frac{x}{y'}=\frac{232323}{370}$

$\frac{y'}{x}=\frac{370}{232323}$

$\frac{y'}{x}=\frac{10}{6279}$

Therefore, ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

4 0

3 years ago

sally has 20 coins in her piggy bannk, all dimes and quarters. the total amount of money is $3.05. how many of each coin does sh

VMariaS [17]

D=dimes
q=quarters

d + q = 20
.10d + .25q = 3.05

d=-q + 20

.10(-q + 20) +.25q = 3.05
-.10q + 2 + .25 = 3.05
.15q + 2 = 3.05
.15q + 2 - 2 = 3.05 - 2
.15q = 1.05
.15q/.15 = 1.05/.15
q = 7

d + 7 = 20
d + 7 - 7 = 20 - 7
d = 13

Sally has 7 quarters and 13 dimes.
Hope this helps!

5 0

3 years ago

10.47kg AND THE OTHER IS 8.23kg. what is the difference????

lyudmila [28]

Answer:

2.24kg

Step-by-step explanation:

Difference=Subtraction

=10.47-8.23

=2.24

So therefore your answer must be 2.24kg

3 0

2 years ago

2. Use the equation 3x + 4y = 2.

IgorC [24]

Answer:

x= −4 /3 y+ 2/ 3

Step-by-step explanation:

8 0

2 years ago

Jamie owns a sailboat rental company, which has a large variety of sailboats of different sizes. He observed that the speed of t

zhuklara [117]

Answer:

Graph C

Step-by-step explanation:

We know the speed is equal to one and a half times the square root of the length. This means that speed is the dependent variable (y), and length is the independent variable (x).

Since the speed, S(x), is 1.5 times the square root of the length (x), we get the function

S(x) = 1.5√x.

When x = 0, S(x) = 1.5√0 = 1.5(0) = 0. This makes it graph C.

3 0

3 years ago

Read 2 more answers