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kolezko [41]
3 years ago
10

Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).

Mathematics
1 answer:
olga55 [171]3 years ago
6 0

9514 1404 393

Answer:

  1. left 1 unit
  2. down 2 units

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

__

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

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Original Figure:
Length = 15
Width = 5
Height = 10
Volume = Length*Width*Height
Volume = 15*5*10
Volume = 750

New Figure
Length = 3
Width = 1
Height = 2
Each dimension has been divided by 5 (eg: 15/5 = 3)
Volume = Length*Width*Height
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The old volume was 750 and it changes to 6
Notice how 750/6 = 125
Which can be rearranged to 750/125 = 6

Answer: if you divide the old volume by 125, then you get the new volume

Note: the new volume is 125 times smaller than the old volume
Put another way, the old volume is 125 times larger compared to the new volume

The fact that 125 = 5^3 is not a coincidence. If you divide each dimension by some number k, then you divide the volume by k^3

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He dimensions are tripled. The new surface area would be times larger than the original surface area.
ddd [48]

Answer:

The new surface area would be 9 times larger than the original surface area.

Step-by-step explanation:

Here we do not know what was the original shape, but we will see that it does not matter.

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The original area of this square will be:

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Now if each dimension is tripled, then all the sides of the square now will be equal to 3*L

Then the new area of the square is:

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So the new surface area is 9 times the original one.

Now, if the figure was a circle instead of a square?

For a circle of radius R, the area is:

A = pi*R^2

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Now if the dimensions of the circle are tripled, the new radius will be 3*R

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Again, the new area is 9 times the original one.

If the figure is a triangle?

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