All categories

2 years ago

The parent function f(x) = x3 is transformed to g(x) = (x – 1)3 + 4. Identify the graph of g(x).

Mathematics

2 answers:

Delicious77 [7]2 years ago

8 0

Answer:

The graph of g(x) will be shifted 4 units up and 1 unit to the right

Step-by-step explanation:

The parent function f(x) = x^3 is transformed to g(x) = (x – 1)^3 + 4

Parent function f(x)= x^3

If any number is added at the end then the graph will be shifted up

If any number is subtracted from x then graph will be shifted right

f(x)----> f(x) + a (shifted 'a' units up)

f(x) ----> f(x-a) (shifted 'a' units right)

g(x) = (x – 1)^3 + 4

The graph of g(x) will be shifted 4 units up and 1 unit to the right

the graph is attached below

Dominik [7]2 years ago

4 0

we have $f(x)=x^3$ which is a cubic function.

and $=(x-1)^3+4$ .

from f(x) and g(x) we know that both are cubic and g(x) has shrink of 1 and up by 4 units in x axis .

You might be interested in

At a track meet, the longest shot put throw by a boy is 25 feet and 8 inches. The longest shot put throw by a girl is 19 feet an

MAVERICK [17]

Its 6 feet and 5 inches

4 0

2 years ago

Read 2 more answers

Sometimes a dilation is an enlargement, and sometimes it is a reduction. Explain what types of numbers for scale factors causes

vovikov84 [41]

If your scale factor has absolute value greater than 1, the dilation is an enlargement.
If your scale factor has abs value less than 1, the dilation is a reduction. 
If the scale factor is equal to 1, the image is congruent to the preimage.

3 0

2 years ago

Read 2 more answers

Rumor of the cancellation of final exams began to spread one day on a college campus with a population of 80 thousand students.S

Nikolay [14]

Answer:

P(t) is directly proportional to N and N'.

Where P is the increase in numbers of students who have heard the exam's cancellation rumor at any time t;

N is numbers of students who have heard the rumor of the exam's cancellation;

N' is numbers of students who have not heard the rumor of the exam's cancellation;

N' = (80 - N). Since the total number of students is 80;

K is the constant of the proportionality.

K is calculated to be 9/700

Therefore,

P(t) = KNN'

P(t) = (9/700) x N x (80 - N)

Step-by-step explanation:

The total number of students is 80. For N, N' = 80 - N.

Initially, 1 thousand people heard the rumor.

Within/after a day, the increased in number of students who have heard the rumor is P = 10 - 1 = 9

P = 9 = K x 10x (80-10)

9 = K x 10 x 70 = 700K.

Divide both sides by 700,

9/700 = (700/700)K

K = 9/700

Subtitle K into the equation P(t) = KNN'

P(t) = (9/700) x N x N'

P(t) = (9/700) x N x (80 - N), where N' = 80 - N

4 0

2 years ago

Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box

Gala2k [10]

Answer:

The dimensions of the box are 12 cm , 12 cm , 12 cm

Step-by-step explanation:

Let x , y and z be the dimensions of box

Volume of box =xyz=1728

$z=\frac{1728}{xy}$

Surface area of box = $2xy+2yz+2xz=2xy+2y(\frac{1728}{xy})+2x(\frac{1728}{xy})$

Let $f(x,y)=2xy+2(\frac{1728}{x})+2(\frac{1728}{y})$

To get minimal surface area

$\frac{\partial f}{\partial x}=0$ and $\frac{\partial f}{\partial y}=0$

$\frac{\partial(2xy+2(\frac{1728}{x})+2(\frac{1728}{y}))}{\partial x}=0$

$2y-2(\frac{1728}{x^2})=0$

$y=\frac{1728}{x^2}$ ----1

$\frac{\partial(2xy+2(\frac{1728}{x})+2(\frac{1728}{y}))}{\partial y}=0$

$2x-2(\frac{1728}{y^2})=0\\x=\frac{1728}{y^2} \\y^2=\frac{1728}{x}$

Using 1

$(\frac{1728}{x^2} )^2=\frac{1728}{x}$

x=0 and $x^3=1728$

Side can never be 0

So, $x^3=1728$

x=12

$y=\frac{1728}{x^2} \\y=\frac{1728}{12^2}$

y=12

$z=\frac{1728}{xy}\\z=\frac{1728}{(12)(12)}$

z=12

The dimensions of the box are 12 cm , 12 cm , 12 cm

5 0

2 years ago

Yesterday, two friends went into a bank to open savings accounts. Allie started by putting $783 in her account, and she will dep

posledela

Answer:

Both accounts of Nick and Allie will have same amount of $864 in time period of 4 weeks.

Solution:

Given, Yesterday two friends went into a bank to open savings accounts.

Allie started by putting $783 in her account, and she will deposit an additional $27 each week.

Nick made no initial deposit, but he will add $288 more each week.

In a few weeks, the friends will have the same account balance.

Here, account balance of Allie for every week forms an A.P as

783, 810, 837, ……. With common difference 27

And, account balance of nick for every week will be

0, 288, 576, …….. with common difference 288

Let, after n weeks the balance in both accounts be equal.

Then, nth term of both series will be equal, we know that, nth term tn of A.P is a + (n – 1)d

Where, a is first term, d is common difference and n is number of terms.

Now, nth term of allie series = nth term of nick series.

783 + (n – 1) x 27 = 0 + (n – 1) x 288

Here, we used same n for both sides because n represents number of weeks and it is common to both

783 + 27n – 27 = 288n – 288

756 + 288 = 288n – 27n

261n = 1044

n = 4.

So, it will take 4 weeks to have same balance and now, substitute n value in nth term of nick series.

$4 \text { th term }=0+(4-1) \times 288 \rightarrow 4^{\text {th }} \text { term }=3 \times 288=864$

Hence, both accounts will have same amount of $864 in time period of 4 weeks

4 0

2 years ago