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The parent function, f(x) = 5, has been vertically compressed by a factor of one-fourth, shifted to the right three units and up two units. Choose the correct function to represent the transformation. A) g(x)=(1/4)5^x-3 +2B)g(x)=(1/4)5^x+3 +2C)g(x)=5^(1/4)^x-3+2D)g(x)=5^(1/4)^x+3+2



Answer :

Compression: g'(x) = (1/4)f(x)

Shift to the right 3 units: g''(x) = g'(x - 3)

Shift up 2 units: g'''(x) = g''(x) + 2

Now, let's put all these transformations in the same expression. Notice that g(x) = g'''(x), since we got g'''(x) after all the required transformations. Then, we have:

g(x) = g'''(x)

= g''(x) + 2

= g'(x - 3) + 2

= (1/4)f(x-3) + 2

Now, we need to use the given expression for f(x) = 5.

Since f(x) = 5 represents a horizontal line, it does not depend on x. Therefore

f(x - 3) = f(x) = 5

(if we shif an infinite horizontal line to the right, it will still be an infinite horizontal line)

Thus:

g(x) = (1/4)*5 + 2

Since this answer is not shown in the options, it seems that there's a mistake in the question. If the given function was, for example, f(x) = 5^x, then the answer would be:

g(x) = (1/4)5^(x-3) + 2

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