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Nostrana [21]
3 years ago
10

The point (1, 1) is on f(x). After a series of 3 transformations, (1, 1) ha been moved to (2, -7). Write a function g(x) that re

presents the transformations on f(x)
Mathematics
2 answers:
harina [27]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that the point (1,1) is on f(x).

Three series of tranformations have been done to get the new point (2,-7)

Note that the three transformations need not be unique.

We can do the transformations in the following order

i) (1,1) is reflected about x axis.  So new point would be (1,-1)

ii) Shift the curve horizontally to the right by 1 unit.  Now new point transformed is (2,-1)

iii) Now shift vertically down by 6 units so that we reach (2,-7)

Thus the above transformations are one of the possibilities.

zepelin [54]3 years ago
7 0
Transformations of functions are simply moving the graph around the plot in the Cartesion plane. It can be done through translations, reflections and rotations. For this problem, 3 transformations occurred from point (1,1) to (2,-7). I think that would be two translations and 1 rotation.

Translation is when you move the point of the graph either horizontally or vertically. The first translation is moving x=1 coordinate to x=2 coordinate by translating 1 unit to the right. Next, you move y = 1 coordinate to y = 7 by translating 6 units up. The resulting point after these two translations is (2,7). The last transformation is rotation of 270° clockwise about the origin. There are already rules for rotations of 90, 180, and 270°. The rule for a 270-degree clockwise rotation is point (a,b) becomes point (a,-b). Therefore, after rotation, the final point would be located at point (2,-7).

In summary, the transformations involved were:
* translation 1 unit to the right
* translation 6 units up
* 270-degree clockwise rotation
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Whitney needed to earn $400 to buy a ticket to a concert. If she earns $15 an hour babysitting, how many hours does she need to
MrMuchimi

Answer:

Shes needs to work 26.67 hours

Step-by-step explanation:

In order to find the amount of time she needs to work, we need to divide the total by the rate that she earns money at. She needs a total of $400 and she gets 15 every hour.

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4 0
3 years ago
A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the box that minimize the amount
Alex17521 [72]

Answer:

Step-by-step explanation:

Let the side of the square base be x

h be the height of the box

Volume V = x²h

13500 = x²h

h = 13500/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2; S =  x² + 4xh

S = x² + 4x(13500/x²)

S = x² + 54000/x

To minimize the amount of material used; dS/dx = 0

dS/dx = 2x - 54000/x²

0 = 2x - 54000/x²

0 = 2x³ - 54000

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x = ∛27000

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Since V = x²h

13500 = 30²h

h = 13500/900

h = 15cm

Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm

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