Given f(x)=x^2, write the equation of the transformed function if g(x)=f(x-1)

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Answer:

1. g(x) = (x - 1)²; translation of 1 unit to the right.

2. g(x) = 3^(x + 1) - 2; translation to the left of 1 unit and translation of 2 units down.

Step-by-step explanation:

f(x) = x²

g(x) = f(x - 1)

g(x) = (x - 1)²

Since x was replaced by x - 1, g(x) is similar to f(x) with a translation of 1 unit to the right.

f(x) = 3^x

g(x) = f(x + 1) - 2

g(x) = 3^(x + 1) - 2

Since x was replaced by x + 1, which is the same as x - (-1), there is a translation to the left of 1 unit. In addition, the -2 causes a translation of 2 units down.

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A two digit number is such that the sum of the ones and the tens digit is ten. If the digits

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Answer:

The original number is 28

Step-by-step explanation:

start by listing all possible combinations of digits that give 10 when added:

19 (1+9=10)

28 (2+8 =10)

37 (3+7=10)

46 (4+6=10)

55 (5+5=10)

Look into the order of digits reversed and what the difference with the original number gives:

1) 19 reversed is 91 then when we subtract 91 - 19 we obtain 72

2) 28 reversed is 82 hen when we subtract 82 - 28 we obtain 54 which is the combination we where trying to find.

Notice as well, that as we go down the list, the differences between reversed digit number and original become smaller (and ends being zero for the number 55), so they do not satisfy the requirement.

Therefore 28 is the answer, since 82 (the new number formed when the digits are reversed) exceeds the original number by 54.

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