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How does the graph of the transformed function ƒ(x) = log(5x+25) compare to the graph of its parent function ƒ(x) = log(4x)?

A. The transformed function has been compressed horizontally and translated 5 units to the left.
B. The transformed function has been stretched horizontally and translated 5 units to the left.
C. The transformed function has been compressed horizontally and translated 25 units to the left.
D. The transformed function has been stretched horizontally and translated 25 units to the left.

User Digeek
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1 Answer

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Final answer:

The transformed function f(x) = log(5x+25) is stretched horizontally due to the increased coefficient of x from 4 to 5 compared to its parent function f(x) = log(4x), and translated 5 units to the left, which corresponds to option B.

Step-by-step explanation:

To compare the graph of the transformed function f(x) = log(5x+25) to the graph of its parent function f(x) = log(4x), let's analyze the transformation. The term 5x suggests a horizontal stretch or compression when compared to 4x, and the additional +25 suggests a horizontal translation.

The multiplier of x changed from 4 to 5, which means the function will be stretched horizontally, as more x is needed for each increase in the log value. Moreover, the addition of 25 inside the log function means that the graph will be translated to the left because the function's argument will reach 0 (the log function's undefined point) at x = -5, instead of at x = 0 as in the parent function. Therefore, we can conclude that option B is correct: The transformed function has been stretched horizontally and translated 5 units to the left.

User Lazar Kukolj
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