Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f as a function of x is equal to the square root of x and g as a function of x is equal to the square root of zero point five x

Given functions are

g(x) can also be written as

And because of 1/2 inside the function with x, there is a vertical compression by 1/2 units .

And that's the required transformation .

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step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: