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zavuch27 [327]
3 years ago
10

Given f(x)=2^x and g(x)=f(x-3)+4, write the new function rule (equation) for function g and describe (using words*) the two tran

sformations that occur between function f and function g.
Mathematics
1 answer:
miss Akunina [59]3 years ago
6 0

Answer:

  • The first thing we do is find out what f(x-3) is
  • f(x)=2^x\\f(x-3)=2^{x-3} this is can be simplified using the rules of exponents
  • f(x-3)=2^{x-3}\\f(x-3)=2^x\div2^3\\f(x-3)=\frac{2^{x}}{8}
  • Then we put that into g(x)
  • g(x)=f(x-3)+4\\g(x)=\frac{2^{x}}{8}+4
  • The first transformation is at f(x), where it is divided by 8, and then inserted into g(x) which increases the new transformed f(x) by 4
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Step-by-step explanation:

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We also know that the total heads (40 heads, each animal has one) plus the number of wings (P*2, each penguin has 2) is equal to the number of feet of his pets (4*C + 2*P, because each cat has 4 paws, and each penguin has 2)

Then we have the equation:

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Now with this, we can find the value of C.

40/4 = C = 10

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Now we can replace this in the equation:

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P = 40 - 10 = 30

P = 30

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