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Elena-2011 [213]
3 years ago
15

The graph of g(x) = |x – h| + k is shown on the coordinate grid. What must be true about the signs of h and k?

Mathematics
2 answers:
9966 [12]3 years ago
8 0

D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer

astraxan [27]3 years ago
3 0

For this case we have:

The main function is:

y = f (x) = | x |

To move the graph vertically we have:

y = f (x) + k

If k> 0, the graph moves k units up

To move the graph horizontally we have:

y = f (x + h)

IF h> 0, the graph moves h units to the left

For this case, we want to move the graph k units up and h units counterclockwise. We have then, the following equation:

g (x) = | x - h | + k

Therefore, according to the definitions:

k> 0

h

Answer:

k> 0

h

Option: The sign of h must be negative, and the sign of k must be positive.

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Answer:

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since the minimum value of x² is 0 (for x=0 ) and for y=1

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then the total area between y=1  and y = 25*x²  is bounded to  x=±1/5 and y=0 . Since there is a direct relationship between x and y , we can find the value of x=a that divides the region in 2 of the same area. thus

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Area below x=C = Total area -  Area below x=C

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∫ 25*x² dx from x=c to x=-c =  1/2 ∫ 25*x² dx from x=1/5  to x=-1/5

25*[c³/3 - (-c)³/3] = 25/2 * [(1/5)³/3 - (-1/5)³/3]

2*c³/3 = (1/5)³/3

c = 1/(5*∛2)

thus

y=25* x²  = 25*[1/(5*∛2)]² = 1/∛4

thus the line y=1/∛4 divides the area in half

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